Good lord! Spare me... So you should get sex by not trying to get sex? That's a f**king paradox, and it's exactly what you're complaining about (doing stuff to try and get sex). Also it's generally what women call a nice guy. A man who thinks that purely platonic acts of friendship will win her favor, and who gets frustrated when his romantic feelings go unrequited. Men who try and follow this advice are doomed to be reviled by men and women alike.
Further, I think you're misunderstanding the situation. She's not mad that he wants to have sex; she's upset that he's sharing her text with his friends. She feels embarrassed and a little betrayed (because the text was for his eyes only). The reason she's embarrassed is because a woman's value is largely tied to her sexual selectiveness. Now his friends think she is, for lack of a better word, a slut. Conversely, a man's value is based on his sexual success. That's why, if the situation was reversed he would be happy that she was telling her friends. She might also feel differently about him because he was too eager at the opportunity to have sex with her. Being overeager means you don't have options, meaning you aren't desired by other women, meaning you must have low value (if you went to the store to buy eggs and there was only one carton left, you would wonder why nobody wanted it). Women intrinsically have value, men only have value in utility. Being desired by a woman delays a man's disposability. That's why promiscuous men are called players, but promiscuous women are called whores.
From that understanding, you can see why this happens:
This stuff about, "he's not treating her like a person" is total bs. Of course she's a person... otherwise she'd be a pocket pussy that he would take out of his sock drawer whenever he felt the need. Instead he's taking the time to get to know her, bringing her on a date, expressing his romantic feelings for her, and hoping that she reciprocates them. That's called courtship, animals everywhere do it. Sex, while not the only goal, is expressly part of it. Other "goals" are intimacy, friendship, support, love, family, stability, fulfillment, respect, personal identity, social status, protection, etc... I will say that sex is the most obvious goal, biologically. It also signifies that the man has proven himself as a worthy mate (once again, women have intrinsic value whereas men have utility). The reason women want to take courtship slowly compared to men is because the vetting process for men is much more rigorous (Will he stick around?). That's all tied up in the relative cost of sex, but this post is way way way too long already so I won't go into it. TL;DR he is treating her exactly how you treat another person, although the lack of discretion is a little obnoxious (but hey I think we can all agree that women are much worse when it comes to being indiscrete about their sexual encounters. There's a reason for it too: men cater to the sensitivities of women not vice versa. Watch the video.).
On a side note, I recently listened to a segment on NPR about infidelity (not TAL) and it was complete horse shit. The woman just spewed the same old line about, "women cheat more than men, but it's the man's fault for neglecting them." Basically, that women have no agency of their own (which feminists always play motte and bailey with). The truth is that women (often) cheat for much more selfish reasons. They see a man who has higher value than their current one and they want his attention. They may stay with their current man because they're pot committed (kids/marriage/house) or because the other male is inaccessible to them for a serious relationship, but they want to switch partners. It's like if you were taking your sick old dog Mr. Pickles for a walk and you see a puppy running around having a blast. So you tie Mr. Pickles to a pole and go play with the puppy. It's fun, this puppy is great! Eventually the puppy's owner comes along and takes it home (it's inaccessible to you for anything more than a little play time). You trudge back to your sick old mutt, let out a disappointed sigh, untie him and say, "Why don't you just die already?" Obviously that's a really ugly thing to do, and people don't think of themselves as being bad people. This is creating cognitive dissonance! Quick, rationalize it! You're a good person, so if you did something bad it must be the man-dog's fault. He's not as fun as he used to be, and girls just want to have fun. The two of you used to play in the park all afternoon long, now he just naps under the window and shits on the rug. He's neglecting your needs, it's his fault that you wanted to ignore him and go play with that puppy. He's a bad dog. If you're not certain, I'm sure your female friends will reinforce the idea. Heck they may even suggest that you put him down. He's not good enough for you.
For the sake of clarity, I don't hate women. I love women, a lot. I do hate bullshit rhetoric like this that obscures the nature of sexual dynamics and confuses men and women alike. There are plenty of women who will truthfully tell you they would be attracted to what amounts to a, "nice guy." But, when actually faced with one they're disgusted (why is he so weak? pathetic? needy? clingy?). Those women aren't liars, they're just as confused as the nice guys. So this kind of bullshit discourse hurts us all.