Lol what? It's like insulting a woman's breast size, and some people have serious complexes about that stuff. Why do you think breast implants are such a huge market and that there are so many ads for penis enlarging bs out there? People can have trama about it, you don't make fun of a person for it. Also in the chance that the conversation was real the girl obviously cared about his opinion due to even telling him her plan. So either they were going out or were just close friends, in either case her comment would probably be taken as a joke, even though it is over the top

It's how she agreed that made it conceited, not to mention there was no reason or point to agreeing like that. The way she responded and acted in the post would normally be taken as rude and conceited

Being curt with "I know" doesn't make someone mad, it comes off as conceit which induces more of a disgust because conceit is a bad personality trait. If you felt compelled to say anything there for whatever reason there were better lines. Some examples: "I get that a lot" "I like to think so too" "It's one of my redeeming qualities" or anything along those lines. But again you can take pride without saying anything, the guy was attracted to her visually so he complimented her in hopes of liking her personality and possibly getting to know her, that's just natural attraction. She immediately thought "fuckboy" and replied in a curt and conceited way, she was obviously not interested in him but she could have just said thanks and moved on anything else was unneeded and rude

Or not, saying "I know" sounds more like they're convincing themselves it's true. Someone with actual confidence wouldn't say that. Also in any compliment whether it be about looks or not saying i know naturally sounds conceited. In a reverse situation where a girl complimented a guy and he said "thanks, I know" everyone would hate that guy. It's like saying "I'm narcissistic, full of myself and to good for you" all in one phrase. Replying like that to a compliment will never be taken as confidence