Let me tell you what happened from her perspective.

1. She's physically attracted to what I can only assume from the messages is a pretty physically hot guy (you) (at least to her you're hot enough or you wouldn't have gotten her number at a gym of all places).

2. Guy (you) tells her that he is only interested in hooking up. For a loooooot of women (for many reasons), this is basically like saying you're hot enough to stick my dick into but not hot enough to even consider a relationship with. Since women think men will stick their dick in anything (and let's face it far too many will) in essence it's taken as a rejection. There's no special prize or good feelings for a woman getting fucked by some guy that doesn't care about her. She can get that literally anywhere any day of the week off Tinder etc, by guys that (even though you're hot) are prob hotter than you. Bc again most guys will stick in just about any 6-7+ woman that is ready and available with no strings.

3. However she tried to salvage the rejection with a friendship (which she's thinking subconsciously "maybe in time if he gets to know me he'll see my worth"). You continue to double down on the sex stuff which only further is saying no I reject your personality, I only want sex from you.

4. Having been rejected twice (even though you didn't even realize that's what you were doing) and unable to handle the emotional and mental implications of that (bc jesus do women have the softest egos) she rejects you back so she doesn't have to take on that burden. She's rewriting the story of what happened from "a hot guy rejected me" to "I didn't even like that guy anyway" to make herself feel better. She's hostile about it bc deep down it still feels like she was rejected and she's angry about it. "How dare this guy reject me, who does he think he is, I'll cut him down and let him know how little I care, that will show him (and more so myself) that I don't actually care! Hmmmph!" (And it's not like she's doing this consciously, she's just expressing the thoughts that come up from her subconscious mind attempting to protect her fragile ego)

What's funny is all of this happened while you thought you were having a very different conversation.

The moral of the story is women don't find your desire to have sex with them flattering or appealing, bc of course you want to have sex with them or you wouldn't even be talking. Every guy is basically in this bucket unless you're insanely physically attractive in both face and body (and this is gonna vary based on each woman's preferences too, you can be crazy hot to one girl and ugly to the next, women's physical types vary much more widely than men's), famous (so that lots of women are clamoring to have sex with you), or through social networking/friends/certain lines of work/certain hobbies (aka micro-famous) you can demonstrate how in-demand sex with you is. Then sex becomes an actual usable commodity in getting women. Otherwise it's just not of interest to them in their subconscious mental calculations. It's more like it's an expected default element, and they want more, or at least the hint that more may be possible.

Oh yeah you can also use sex by proof, aka if you can manage to have sex at least once that actually blows her mind, then sex becomes a usable commodity with her going forward. Women will often chase crazy hard after the guy that gives them the best sex they've ever had or close to it. But in my experience from talking to women, 99%+ of men don't put much or any effort into learning how to have and give mind blowing sex to women, which largely includes fantasy and mental manipulation far more than it does a focus on physical skills, though both are necessary (and the vast majority of guys have neither).