art is not an excuse

The one thing I came out of art school with that has been invaluable above anything else I learned there was the ability to not only give but receive a critique. It's a skill that I really wish was part of the general educational system - the ability to take a thing you made, put it up in front of a group of your peers, and take their opinions on the thing gracefully, and without taking it personally.

You are not your work. You created it, it came from you - and that's where the realtionship ends.

In order to successfully give a critique, it's important to list the good with the bad, and not be overtly hostile about it. "I really like your use of color but your message would come across better if you worked on realistic anatomy more." "You're dancing is really expressive, but your arms are a little sloppy and working on that would really clean up your presentation."
What's good, what could use work, why it needs work, and how it would help.

In order to successfully receive a critique, you have to listen.
Actually listen. Open your ears and hear what people are saying about what you did.
Take it in, soak it up, and utilize the information.

Also, don't ask for a critique if you don't actually want to hear one.
A critique is not the place for gratuitous back patting - that's what your mother is for.

There is a general (and correct) assumption that if you ask for feedback it is because you want to improve what you're doing in some way. With the exception of internet trolls (hello trolls!) most people are going to give you honest and useful feedback. Throwing that feedback back at them and refuting it as wrong because of X, Y and Z is not only insulting (you did ask for feedback after all) but does a disservice to you and your entire art community. And it makes you look like a whiny brat. "This Is Art" is not an excuse. It's not a defense. Every artist everywhere has to defend their work - has to explain the reasons behind color choice, composition, and concept; and not everyone is going to agree with your decisions. It doesn't mean your decisions are wrong, but neither does it make them correct - and it's worth listening to and contemplating to get a outside perspective so that you can make your art communicate better.
"But I don't make my art for an audience, I make it for myself."
Then why did you put it in public in the first place?

It's a hard lesson, and a hard threshold to cross for a developing artist - finding a balance between what you want to do, and what an audience wants to consume. If you truly don't care about an audiences opinion, that's perfectly fine - but you can't go and expect people to fawn over your creation just because you call it art - as a dancer you can't expect to get hired to perform if people don't actually enjoy watching you dance on some level; as a fine artist you can't expect to get a gallery show if no one is going to want to buy your work.

Art is in the eye of the beholder.

And critique is actually pretty easy. Practice with your friends. Turn it into a drinking game if you must but learn how to do it and receive it professionally. Someone not liking your work is not a reflection on you or your personality or your validity as a person or as an artist. It simply means they don't like that one thing you made; and they are under no obligation to like it.
And I'm not advocating pandering to the mass market either.

Just don't be a brat about it.