It's not narrow minded, it's science. Your parents raise you for several years, and your interactions with them are what give you your personality. Your interactions with others only change it slightly, not to a large degree.



For example, if you are raised being told you're better than everyone else, if you are given everything you want, and if you see your parents mistreat others, you will grow up to be a spoiled, entitled brat that treats others poorly because that's how you were taught. (Diamond Tiara)



If you are raised by parents that do not tell you "no", and do not stand up for themselves, you will grow up to take advantage of them because you know that they will not refuse you. (Zephyr Breeze) (But that, too, was an extremely shitty episode, because it does not explain why Fluttershy is the way she is. Your personality is not genetic, and cannot be inherited through DNA from your parents. Making Fluttershy's parents the way they were has the same exact problem as Rainbow's parents. It's not believable if you have a grasp on psychology.)



If you are raised by parents that foster your interests and push you to excel, and have a role model to look up to and emulate, you can do great things. (Twilight Sparkle)



However, if you are raised by parents that do not push you to get better, that do not foster your interests, and do not critique your failures, you will grow up to be like a vast majority of people: the ones that do not have large aspirations, the ones that do not know what they're great at, the ones that do not strive to push themselves to being great at anything. These are Rainbow's parents, but this is not Rainbow.



Have you ever watched a sports coach give a speech to their players? They're NOT nice. There is a reason for that, though, and it's to force the players to get motivated to play better. Coaches will yell all the time. They will tell players what they're doing wrong, and how to fix it. They will push players to the brink of exhaustion and past their limit, because only through challenging yourself can you get better. It doesn't matter WHAT it is, you HAVE to challenge yourself. Military instructors are the same. They will yell and criticize everything you do, every minute of every day. They will make you do an unconscionable amount of PT (physical training) and they will constantly be in your face if you fuck up. They don't do it because they hate you, they do it to make you be the best damn military member you can be. It is a tried-and-true method of getting people to do things they'd never dreamed they'd be able to do. If they coddled you the way Rainbow's parents do, you would NEVER amount to anything. It's psychology. You HAVE to be motivated. You HAVE to be challenged. Rainbow's parents CAN'T do that for her. Which is why they were written incredibly poorly.



But please, do go into full rant mode and explain how coddling Rainbow for the first several years of her life could force her to be better. I'd be interested in hearing what you think.



Also, the only time we see Rainbow deal with bullying as a filly is when the bullies were picking on Fluttershy. She would not have the confidence needed to stand up to them if her parents coddled her for her whole life. She would not have the skill or technique to beat the bullies in the race. But, if she had parents that critiqued the things she did and pushed her to be better, she WOULD have both the confidence, AND the skill, required to stand up to the bullies.