@OniBarubary It's not that Yagen is tired of the social implecations of being a Man; it's that he was suddenly thrust into a position of power, "The Banchou", just for being his normal self, a tough delinquent. He was going about his daily life, but now he carries the hopes and expectations of Harikura on his shoulders. In the end, he crumbled under the weight of the responsibilities. The title "Yagen Unleashed", refers to the moment Yagen was seperated from his responsibilities as Banchou, it's a flashback episode. This is where Yashiya comes in. She's someone who doesn't see him as great, but as dirt, which acts as a release to all the responsibilities he had gained, making him Free, as he said, "I've been released". While toxic masculinity is awfull, I feel the author only brought manliness into the story to claim that Yagen turning his back on his friends to take the route that was easier for himself was Un-Manly.
Now, going into infferences/speculation, the non-toxic approach would be to level with his kouhai on the situation, and they create a solution together. Heck, Yagen could have even ATTEMPTED the peace talks, instead of just running away. But being a deliquent school, he'd be percieved weak, and lose face. That fact wasn't hinging on manliness, but on the expectations of a banchou, and what it means to stand at the top. If people see that you're human, that you really can be beaten, then there's no reason to listen you, and they'll aim for the position of banchou, or another school will take over yours. It's lonely at the top...
Rokudo shows that you can be weak, but have strength through relying on your friends.
Tldr: Yagen's troubles stem from being strong, not from being a man. While there are overlapping symptoms to toxic masculinity, it's a different disease.