He was feeling insecure and often times in relationships things like insecurity, jealousy, etc. can breed resentment towards the person that you are with and Honda no longer felt like he was worthy enough to be with Kaido so he wanted a break to work on himself and reflect.
Also. Because kaido’s workplace discovered he was photographed with a “friend” and people found out he was gay, since in Japan there’s obviously a stigma against people of sexual orientation, therefore Honda didn’t want to get in the way of his partner’s dream like he hurt him before in highschool. So he decides to leave but really He’s just insecure that he can’t be by his side anymore since he’s off to do great things in his career.
It was sooo lovely but I'm still confused why Honda broke up with Kaido. I could not catch any logic in this part