Why do girls want to cuddle in public?

She's just claiming territory. Which I personally think is extremely annoying and a little bit rude. It's one thing if she gives you quick embraces every so often, but to snuggle on you all lunch period is over the top. She sounds clingy. It's actions like this that often translate into jealousy problems later down the road. Good luck, lol.

because she showing you off and wants you to like. show her off too and be proud that your with her. also it could be that she's proving to everyone that your 'happy and in love'

most women are very touchy and clingly.

Yeh, she's making a public declaration and using bragging rights that you are hers and she is yours. If I were a guy, that would turn me off, especially if she keeps it up. She may even be a little insecure.

The reason why she does it is to attract attention to you two. She wants people to stare and show you off, and to prove to herself and others that she can get a boyfriend. I personally find it kind of awkward doing that in public, especially school. A little hug/kiss here and there would be alright, but when it comes to touchings and cuddling, nahh huh. Not my style.especially when people are eating lunchhh.
Anyways, I hope my analysis helped! But its your opinion on what you want to do.

Depends, if it's like a lead-up to making out I'd think that you just like each other so much that you can't keep your hands off each other and waiting until after school is too long. But judging from your reaction that doesn't really seem to be the case. I'm guessing she's just trying to show everybody that either:

A. You're hers , and telling all the other girls to back off.

or

B. She's yours, and needs that self-esteem boost by showing you off.

I don't think she does it to annoy you. More like she's proud you're her boyfriend and yeah to tell everyone that you're hers. Also, maybe because your her first one so she doesn't really know how to act or how to make her relationship with you more personal. Sort of a combination. It's little immature.

she wants to flaunt you probably.

i hate when girls do that