Heres some background:
I go to college with this chick I got her number we both found each other attractive etc. But every time i try and set something up she tries to avoid answering the question, shes really shy i guess. Idk what im doing wrong or if i should just give up. I know shes attracted to me from previous conversations but that doesnt seem to mean much. We both dont want relationships we both just want to fool around.

ME:Hey (her name)! ;p

HER: hey (my name)!

ME:how was your weekend?

HER: it was gooood real fast tho hbu??

ME:it was fun had a few beers yesterday bought a new sweater haha sucks we have classes tomorrow

HER: haha I saw u drinkin on snap haha oooo ur outfit games are on point haha and I no I hope the snow gives us a delay

ME: Thank you! And im soo done with the snow i cant wear loafers because ill end up face planting on the floor

HER: hahaha aww! if it makes u feel better I fall no matter what I wear

ME: i bet you still look cute while your slipping around lmao

HER:haha nahh

ME: got anything special planned this week?

HER: besides class haha not that I know of hbu

ME: Other than classes and the gym I’m free, we should figure out a time to grab bite to eat together.

HER: gains bro haha

ME: Whats your Tuesday look like?

HER: night class with ur boy

ME: you aren’t free before that?

HER: I'll let u no love

ME: Okay sounds good.

I really dont know what im doing wrong i kept it short and sweet included her name stayed persistent when she tried to avoid my question.

Really not great at this but few things I noticed:
She seems to type haha fairly often, which seems to me is being used in the awkward filler and possible approval seeking sense by both parties. Kind of like how I assumed you used it with something with no real humor "ME:it was fun had a few beers yesterday bought a new sweater haha sucks we have classes tomorrow".

Gains ''bro'' seems a little friendzoneish, especially since she also used it to avoid your proposal entirely.

"ME: got anything special planned this week?

HER: besides class haha not that I know of hbu

ME: Other than classes and the gym I’m free, we should figure out a time to grab bite to eat together.

HER: gains bro haha
"

Since you had other subjects besides just 'wanna hang out'? She had a somewhat easy out to avoid the question, so I would avoid that in the future. One thing I have heard suggested is don't ask are you free x day, because like now they can just say uh maybe/idk/ill let ya know/nope. If you ask something more of 'when are you free this week/when you free to hangout' it at least avoids the awkward, oh well how about y? No? How about z? This girl doesn't seem that down at this point though, so I wouldn't be surprised if she still said 'maybe(no), I'll let ya know(no)'.

Other than that maybe next convo try to get her to talk about something more specific that she's into/passionate about, or have a bit more fun with the conversation.

Instead of saying "what's your Tuesday look like?"

Try something like "What day works best for you?"

what charles said, but i give them options, so is friday good for you or is sat better? get them thinking about when they are free rather than if they are free for you

also you are showing too much interest, girls like to chase not be chased

I read online that you can try to assume the meet up with the girl as if it's going to happen.
Example) "Drinks and dancing at Club X tomorrow night 7pm."

Or you could ask if she has any plans for the weekend, like you did, and then assume that the meet up is going to happen.

Your goal right now should be to simply invite her somewhere more specific location and time wise, then seeing how she replies.

Let us know how it goes

It's the opposite of this. The way of the world for millions of years across basically all species.

Really? please explain how you came to that conclusion?

Real life observation and implementation, and biology books.

ok then,

You didn't do anything wrong you goof !
Guys stop over analyzing shit and trying to guess what another person is thinking because you'll never ever get it right !
Go with the flow, I sensed good vibes from that, just stick to your guns and keep talking to her whenever you want.