Anyone who knows me knows that I don't like to be criticized, and I'm not just talking about dance! I tend to take general comments as cutting remarks, and combined with my hot temper, sarcastic tone, and tendency to become defensive and condescending when arguing, it doesn't always end well. What I've learned to do over the years of dancing is how to take criticism on my dancing, and it's helped me take criticism better in general. Well, I'm working on it, and I hope I can help you too.
Don't take it personally. They're just trying to help.
Your teachers aren't out to get you, most of the time. Some teachers are just not nice people, and they will make cutting comments just because they can (I had a teacher who told one of my good friends that she "liked her dancing but didn't like her personality"). I used to cry because of comments that my ballet teacher made in class, but I learned that if I separated my personal life from the classroom, the need to cry stopped. However, 99% of the time, your teacher is making the comment because there was something that could be improved. Even if they're yelling, it's not really you they're yelling at as a person, they're yelling at you as a dancer. On that note...
Leave your personal life at the edge of the dance floor.
When you step into the studio, you're there for class, not to mope about the 10 page paper you have to write tonight or the fight you just had with your boyfriend. I definitely went into class in a bad mood a few times and it made it that much harder to take criticism. If you come in with a positive attitude, forget the world, and just focus on your love of dancing, you'll not only feel better about yourself, but you'll improve as well!
Similarly, leave your dance life on the dance floor.
Don't go home and cry about your ballet teacher not liking your hip alignment in class. It's not worth it. And the more you cry and blame the teacher for hating you, the less you'll look at yourself and improve whatever the teacher was trying to get you to do.
Teachers criticize you because they care about you.
Why would a teacher waste their breath, their time, and your money to make a comment to you if they didn't care about making you better? If they think you're a lost cause, they won't spend 5 minutes trying to get you to stretch your foot without curling your toes under. They criticize you because they think that whatever they have to say will make you a better dancer, so take their comment as the gift it is and improve yourself. A little girl in the class I used to assist would always cry when the teacher would "yell" at her to correct something, and the teacher was always nice enough to tell her afterwards that she just needed to make corrections when criticism was given. Your teacher may not be as nice, so make sure you try to correct things as soon as you get the criticism in order to avoid further conflict.
I've been hinting at it this whole time, but the teacher said something for a reason - there's something to be improved.
Why else would they say anything, if what you just did was perfect? News flash: no one is ever perfect. I've seen videos of prima ballerinas who complain about their stability or where their hips are. There's always something that can be improved, and the moment that you stop remembering that and start blaming your teacher or being hurt about the comment is the moment that you will stagnate as a dancer. You'll stop improving if you don't realize what there is to be improved.
Keep in mind that if a teacher does comment on you personally, it may not be your fault.
If the teacher tells you to lose weight, to take off your cute pink sweater, or that they don't like your tone when you talk back, okay, that's probably your fault (unless you're not actually overweight). But if the teacher tells you to stop being stupid and do that quadruple pirouette when you're not having a great turning day, that's not your fault. Don't take it personally, you're not stupid. But you may not be trying as hard as you can either.
I hope these tips have helped! Taking criticism is how we dancers survive (boy, am I in the wrong field, huh?), so just try to realize that criticism makes you better and is not designed to hurt you emotionally.