[Want nonjudgmental parenting advice and personal stories for all kinds of families? Sign up to get NYT Parenting in your inbox every week.]

“People do not think that men can parent,” said Marshall Forstein, the interim chair of the department of psychiatry at the Cambridge Health Alliance, and an associate professor of psychiatry at Harvard Medical School. Dr. Forstein, a father of two, adopted his first child more than three decades ago with his husband, who is no longer alive. “There is an association of homosexuality with deviant culture.”

Mr. Cohen declined to comment for this article, but he has not been shy about addressing his critics. During an interview on Howard Stern’s SiriusXM radio show last month, he shot back at the naysayers who chastised him for taking his newborn son aboard an airplane. “You don’t think I checked with three pediatricians before?” Mr. Cohen said, using profanity to punctuate his point.

(Also, the critics may not realize that New York State does not allow for paid surrogacy arrangements, so would-be parents like Mr. Cohen go out of state — in his case, California — to find a surrogate. How else would Mr. Cohen take home his son?)

Mr. Cohen has also replied directly to his Instagram critics. After someone chided him for taking Benjamin “out into the world too soon” (on a photo of Mr. Cohen going for a dog walk with his son), Mr. Cohen wrote back: “My pediatrician told me to take him out. And this was Friday when it was 55 degrees. What else you got?”