Shinshom is on-point here. Regardless of Adachi's flawed perception on women and girls, he still generally treated Kyo as at least a positive acquaintance since the start, with a few dumb moments motivated by his infatuation for Anna, but otherwise seeming to have a positive view of Kyo, and growing into a friend (I think of when the seating got changed last time before the end of their 2nd year, when Adachi, Kyo, Anna, and Hara were all sat together, and Adachi seemed to be pretty friendly with Kyo, even if Kyo was less than friendly) before even approaching him about getting insider info on Anna. That moment was just about when Kyo maybe started realizing they were closer than just random classmates, and often the manga is flavored by Kyo's perceptions, but we need to realize there's more to this world than what Kyo sees with his flawed perception, always downplaying how close he is with people (though that's been changing, and is much closer to reality by this point).
Adachi has problematic perceptions of the girls in his grade, for sure, but he's generally been pretty straight with Kyo, with Kyo being the one that imagines the worst of the guy. Like the note-passing that Kyo thought was some form of bullying that involved asking Anna if she did something nasty, when it was just a signed request for her LINE, so it wouldn't even be something that would be misconstrued as from Kyo, anyway, let alone something that would ilicit a horrifically negative response from the girls.
There was no ill will for Kyo in Adachi having him do that. In fact, it can be argued he was trusting him to follow through with a relatively innocent request, and Kyo was the one that warped things into him 'defending' Anna from a note-based request she had no obligation to comply with, anyway. Sure, we are happy he ended up giving her the sketch he made based on her, since it elicited a positive response from her for Kyo, but he didn't necessarily need to do that, once the full context was known. Even Kyo realized he did a fairly unnecessary thing immediately after the fact.
Edit: Shit... people misunderstanding this challenge reminding me of people in comments misunderstanding why Kosaki confessed near the end of Nisekoi. She already knew Raku's heart was already made up- she could read the signs in the things he was saying to her about Chitoge leading up to when she finally confessed her feelings to him. She knew she was going to be rejected. So, yeah... sometimes doing something isn't about some 'last ditch effort to win', it's just something you do because you feel you just have to do it, even if you know it won't change anything. Either your own peace of mind, closure, whatever you want to call it. Adachi just needs to do things this way so he can be at peace with Kyo and Anna being together in his own way.