The following is a script from "Switching Teams" which aired on April 10, 2016. Lesley Stahl is the correspondent. Shari Finkelstein, producer.

Just two years ago, Schuyler Bailar was one of the fastest high school swimmers in the country -- a champion breaststroker with a stellar academic record who had women's swim coaches from around the Ivy League coming to call. Schuyler's first choice was Harvard, and as luck would have it, the Harvard women's swim team was in need of a breaststroker. Schuyler was offered a spot, and a seemingly perfect match was made.

Schuyler Bailar CBS News

But when Harvard's swimmers hit the pool deck this past fall, Schuyler had switched teams. Schuyler now swims with the men. The story of how Harvard came to be the first men's Division I athletic team in the nation to include an openly transgender young man is also the story of a bigger transformation -- in attitudes, acceptance, and the larger conversation about what it means to be transgender.

Lesley Stahl: How different are you? If I had met you a couple of years ago and then saw you today?

Schuyler Bailar: Physically you'd say-- yeah, you might not recognize me.

Lesley Stahl: You look that different?

Schuyler Bailar: I'd say so. Yeah.

We'd say so too. This is what Schuyler Bailar looked like in high school. From the outside, Schuyler back then appeared to be a young woman who had it all -- outstanding grades in school plus all-American times in the pool -- an attractive combination to swim coaches from top-notch colleges.

Schuyler Bailar Personal photo

Stephanie Morawski: She was a very strong breaststroker, and those times were fast.

Harvard women's coach Stephanie Morawski traveled to DC to recruit Schuyler.

Lesley Stahl: First impressions?

Stephanie Morawski: She was engaging, energetic and she was somebody that I really thought would do well at Harvard.

Harvard was Schuyler's first choice. But this fairytale had a little wrinkle, one that may have started before Schuyler even learned to swim.

Lesley Stahl: When you were a little girl, were you a typical little girl? Two, three four--?

Schuyler Bailar: Definitely no.

Lesley Stahl: Even three, four, five?

Schuyler Bailar: My parents dressed me in pink dresses and bow ties, and I had a doll. But I don't think I was typical even then 'cause I would-- I would like to rip them off and I didn't want to wear the dresses.

Gregor and Terry Bailar CBS News

Gregor Bailar: "I'm not wearing a dress."

Gregor and Terry Bailar are Schuyler's parents.

Lesley Stahl: Did people think Schuyler was a boy?

Terry Bailar: All the time.

Terry and Gregor just assumed Schuyler was a tomboy who preferred short hair and hanging out with the guys. That their daughter might be transgender never occurred to them, though there were clues. In middle school, Schuyler's class had to make self-portraits in the present and the future. She came home with this.

Schuyler Bailar's art project CBS News

It made no sense at the time why the future meant becoming an old man with a mustache. And the confusion only worsened when puberty hit, and things like breasts began to appear.

Schuyler Bailar: I was like, "That's not something I want. And I don't really know why, but I just know I don't want that."

Even though it felt wrong, Schuyler saw no choice but to try and make it work as a girl: with long hair and dresses. But it backfired. She developed major eating disorders.

Lesley Stahl: Bulimia? Anorexia?

Terry Bailar: Both.

Lesley Stahl: Both?

Gregor Bailar: Yeah. It was serious.

Terry Bailar: We feared for his life.

Gregor Bailar: Yeah.

They postponed Schuyler's going to Harvard and got her help at an eating disorders program. When she went to hear some transgender men speak at a local church, wham! Everything started to make sense.

Schuyler Bailar: I was like, "Holy crap, this is me. Like, this has-- this is 100 percent, everything that they're saying, that's me." And I just melted down. I just started crying and sobbing. And my dad was picking me up 'cause he was coming to visit me.

Lesley Stahl: That very day?

Schuyler Bailar: Yeah, and I walked out to him and I said-- and I was sobbing, I was like-- and he just hugged me.

Gregor Bailar: He came out, you know, in tears--

Schuyler Bailar: And-- eventually he said, "D-- like, what's-- what's wrong, Schuyler?" and I said, "Dad, I think I'm transgender."

Lesley Stahl: So how did you handle it?

Gregor Bailar: I hugged him. And he cried and cried.

Schuyler Bailar: It just made me realize, like, I wanted that so badly but I knew how hard it was gonna be. And I-- I was like, "What about swimming? What about my body? What about surgery? What about the money? What about people? What are we going to say? What about my grandparents? What about my brother?" Like, everything at once. I was like, "But I want this, and I know I want this."

Schuyler's mental health improved quickly. But there was still the matter of telling Coach Morawski that her new women's swimmer would now be coming to college as a man.

Lesley Stahl: So what was your reaction?

Stephanie Morawski: I was surprised. But the-- really, the big question Schuyler had was, "Can I still swim on your team?"

Lesley Stahl: What did you think? Did you think someone who identified as a man could swim on the women's team?

Stephanie Morawski: I thought logistically we might have some issues that we'd have to work out.

Like NCAA rules. Turns out the NCAA has a policy that allows for athletes who identify as male but were born female to compete on a women's team as long as they don't take male hormones. So Stephanie Morawski said yes-- and Schuyler started making plans to live something of a double life: to be a man on Harvard's campus the next fall, but a woman on Harvard's swim team. Meanwhile Schuyler came out as transgender on Facebook, and posted on Instagram that he had so-called "top surgery" -- a double mastectomy to remove the breasts he hadn't wanted. The whole situation started to worry Coach Morawski.

Terry Hong: I think Stephanie was the first to realize that Schuyler's plan of being a woman in the water but a man outside was going to be--

Gregor Bailar: Difficult at best.

Terry Bailar: --totally detrimental to her psyche.

Stephanie Morawski: When you enroll in college, it's an opportunity to start over again.

Lesley Stahl: You can reinvent yourself.

Stephanie Morawski: You can reinvent yourself. And I was struggling watching Schuyler, because he wanted to reinvent himself as Schuyler as a male, but was being held back by the athletic piece of it.

She discussed her concerns with her friend and colleague, Harvard men's swim coach Kevin Tyrrell.

Stephanie Morawski: Kevin was-- just kinda looked at me and said, "I don't-- I agree with you, I don't think that you can have a dual identity. Why doesn't he just swim for my team?"

Lesley Stahl: Just like that.

Stephanie Morawski: Just like that.

Kevin Tyrrell: I mean, it made sense, right? If you're happy being a male-- and that's what you want to identify as, then it makes sense to be on the men's swimming team.

That would be allowed under NCAA rules -- and he'd be permitted to take testosterone. But before giving Schuyler the option of joining the team, Tyrrell called a meeting of his swimmers to discuss what he thought would be a very sensitive issue.

Lesley Stahl: And what were the reactions?

Kevin Tyrrell: They didn't see it as a big deal. I had worked up all of these questions in my mind to ask them, and I asked them, and they were like-- "That sounds fine."

When they didn't even express concern about the locker room, Tyrrell wasn't sure he believed them.

Kevin Tyrrell: So I concluded, "Well guys, you know, let's-- come into my office, you know, if you want to talk to me one-on-one, please do."

Lesley Stahl: You thought some might be holding back?

Kevin Tyrrell: Right. Just 'cause of group think and-- and then so, no one came into the office.

Lesley Stahl: And it surprised you?

Kevin Tyrrell: It did surprise me. You know, I swam in college over 20 years ago and I think it would have been a different process for me.

But choosing between the women's and men's teams was agonizing for Schuyler, who was used to winning as a woman. On the men's team he'd be at the back of the pack.

Stephanie Morawski: Schuyler had to do a lot of thinking about what mattered most. Was it breaking records, or was it really being happy?

Lesley Stahl: You put that to him.

Stephanie Morawski: I did.

That was last spring.

[Announcer: "For Harvard in lane 2, Schuyler Bailar"]

This fall, at Harvard's meet against Ivy League rival Columbia, we watched as Schuyler got ready -- scars visible across his chest -- to step up onto the starting block to swim with the men as a man.

Schuyler Bailar prepares to compete CBS News

Schuyler Bailar: My goal to myself, because it's not realistic for me to win anything right now, at all, is to try to beat at least one person in every race.

Lesley Stahl: And have you met that goal so far?

Schuyler Bailar: Almost. Yesterday, I did get last in my second event. But-- but that's the only one. And I've done eight races. So, seven out of eight of them I've gotten not last.

Lesley Stahl: That's-- I-- I'm really surprised.

Schuyler Bailar: I'm really happy about it.

And he's happy about living as a man in all facets of his life. He takes the NCAA-approved dosage of testosterone which has been lowering his voice, broadening his shoulders, and bringing him closer to that future he had envisioned back in middle school.

Lesley Stahl: You have a little mustache?

Schuyler Bailar: Yes, I have a little mustache, little peach fuzz.

Lesley Stahl: Are you shaving?

Schuyler Bailar: Yes. And I shaved because I wanted to look nice for the interview.

Schuyler has been remarkably open about all this, chronicling the whole process of his transition on social media, complete with before and after images. And he's invited people to ask when they have questions.

Lesley Stahl: You are almost passionate about answering questions.

Schuyler Bailar: Yes.

Lesley Stahl: You don't run away from this.

Schuyler Bailar: People are ignorant. Period. Because it's not taught in school. Like if you don't know a lot of trans-people how are you supposed to know the answers to the questions about people who are transgender?

Lesley Stahl: What kind of questions do you get?

Schuyler Bailar: Do you still have a vagina? Like, people like to ask that one. And a lot of people get really uncomfortable, like a lot of trans-people hate that question.

Lesley Stahl: You don't hate that question?

Schuyler Bailar: I don't like it, but I try to see it from their perspective. And I'm like, OK, if they-- if, like-- if I were in their po-- like, their position, I'd probably be wondering the same thing.

Lesley Stahl: Well, what's the answer to the question?

Schuyler Bailar: Yes. I mean, that's the answer to the question.

Lesley Stahl: That's the answer--

Schuyler Bailar: It's, like--

Lesley Stahl: --to the question.

Schuyler Bailar: It's a simple question.

He says being transgender has nothing to do with whether or not someone gets "bottom surgery," and it also has nothing to do with sexual orientation. Schuyler has always been attracted to girls; in high school, as a young woman, Schuyler had come out as gay; now, as a man, he's straight. But there is one small matter we discovered, where he's leaving his options open.

Lesley Stahl: You will never get pregnant.

Schuyler Bailar: I don't know about that. That's a long story.

Lesley Stahl: Really?

Schuyler Bailar: I-- I-- there are, there are trans-men that get pregnant because they want to have biological children.

Lesley Stahl: So this is in your head, that one day you might give birth?

Schuyler Bailar: Might is-- is in bold-- and underlined and italic-ed. But yes...yeah. I don't know. I'm 19.

19 and healthy. Back at that Harvard-Columbia meet we went to, Schuyler achieved his goal of beating one swimmer and he beat his own previous best time by more than a second. But we did notice Schuyler during the women's competition, cheering on his would-have-been teammates in his old event. And we were pretty sure he noticed that his old times would have won first place.

Lesley Stahl: Have you ever in the whole time second-guessed what you did?

Schuyler Bailar: I think I'd be lying if I said no.

Lesley Stahl: So you have.

Schuyler Bailar: I know I made the right decision. But I think sometimes I, like-- I'm like, "Oh, I really wish I could-- I could compete as a girl. Because I want to win that race." It's fun to win, and it's something that I worked really hard for. And, you know, I work the same amount. But now I'm working the same amount for 16th place, you know?

Lesley Stahl: And that's OK?

Schuyler Bailar: And that's OK. It's the way it is. And it's also a lot of fun. It has other kinds of glory in it.

Lesley Stahl: Different kind of glory.

Schuyler Bailar: Definitely a different kind. It's a glory that, like, fills me inside.

Lesley Stahl: Compared to one year ago, how are you feeling?

Schuyler Bailar: Proud. In one word, proud.