I feel like we need to talk about the fact that while Akito did have a misogyny issue prior to Vivid BAD SQUAD's formation, it is not why he viewed Kohane as ill-fitting for An.
Akito was upset that Kohane partnered with An because he learned this information right before he was about to ask An to team up with him and Touya. We know he was planning on this because the subtext makes it obvious— the previous chapter has Kotaro talking to Akito about the possibility of teaming up with An (which Akito acts aloof about), and Akito opens his conversation with An the next day by asking her if she's found a partner yet.
Learning that An has paired up with Kohane bruises Akito's ego, and more importantly, challenges his entire worldview. He's always been treated horribly for his lack of skill in Vivid Street, and holds himself to unreasonable standards for a variety of reasons. He believed An was the same as him, due to the fact that they both saw RAD WEEKEND and were the only people dedicated to surpassing it from back then. We learn retroactively (in Find a Way Out) that the source of Akito's trust and respect in An is for the fact that she was the one who refined his dream into "surpassing RAD WEEKEND" rather than "making an event like RAD WEEKEND." Akito viewed teaming up as a way to be collectively stronger, and felt completely betrayed by An pairing up with Kohane, who has no experience with music.
Note: While Akito did team up with Touya, who was new to street music, Touya does not have the same context as Kohane. Unlike Kohane, Touya has had years of musical training, even if it wasn't with street music. Akito's questions about Kohane are pointed towards both specific experience with street music and experience with music in a broader sense.
It's the fact that An is deliberately hindering herself in Akito's eyes that makes him feel so hurt. And the reason why he treats Kohane that way, why he wants to crush her, is because he is projecting himself onto her.
He sees his own past inexperience and insecurity in Kohane, his past inability to "be serious" after quitting soccer, and thus wants to "teach her a lesson" by essentially recreating what happened to him at Crawl Green.
In my opinion, Akito's behavior would remain the same even if Kohane was a boy. It was not triggered by a perception of Kohane as frail due to her gender, but rather by a perceived betrayal from An. He can't understand why she, an individual he trusted and believed in, made a decision he thinks is counterproductive.
This is furthered by what happens after Akito chases Kohane off and self sabotages after the blackout. Akito comes back to WEEKEND GARAGE the next day, trying to talk casually with An again, as if what he did was no big deal. He still wants to trust her, now that he's gotten rid of the "problem". This obviously doesn't go over well with An, who also trusted Akito but now feels betrayed by him due to his actions.
However, it's time to acknowledge the elephant in the room: this is Akito acting on An's behalf, because his instinct is to trust his judgement over hers. In other words, this is behavior rooted in misogyny!
His trust in An is something reiterated numerous times in the story as something that is unwavering (mostly after Main Story). Even in Main Story, he has no reason to doubt An here outside of his own projections. The fact that he does is an indication of misogyny (i.e. he sees his logic and behavior as inherently more sound and reasonable because of his gender, and he needs to "protect" An from continuing to pursue a "mistake" instead of teaming up with him because she is a woman), especially because he takes a similar action in Ena's first event— when he talks to their dad about treating Ena better without her input.
Note that An also has misogyny and gender as a much more relevant topic to her character than Kohane (for Kohane it is slightly relevant, but not super much). This is why I think this interpretation is more sound narratively. Thank you for reading.
TLDR: Akito was not displaying misogyny towards Kohane in Main Story, it was towards An.
