Rei shouldn't have time for club activities. He needs to do his schoolwork like any student, but he also needs to handle all the domestic work at home, seeing how he's living on his own. Above all, he needs to spend a whole lot of time on shogi, lest he loses the pro status, which he, in fact, is in a danger of doing. So, how does a shogi club benefit him in any way? The ADHD teacher just wants him to make friends and to get free shogi lessons from Rei, but he seems unable to grasp the reality of Rei's everyday life. It's like he suddenly forgot Rei can barely attend school enough to avoid repeating years.
I get the teacher means well and has spent a lot of effort to keep Rei company and give him mental support, but he's too ADHD with his decisions.