Comment by Waitwhat on Boy's Abyss - Chapter 82

I think Kazu was having s** with someone and the mom was listening. The shoe when Rei got home, the background noises, and the mom saying to not mention knowing since he'll be embarrassed. The way she phrased it ("found out") makes it seem like this is not a one time occurrence.

His mother listened when Kazu was talking with Reiji about leaving town and that he was jealous of Rei for having slept with his teacher. The mother probably introduced Kazu to a women to keep him in town.