Something is not right about KyoujiKyouji at first looks like your typical nice guy archetype being polite, smiling all the time and who is generally known for being nice. This image holds pretty well during the first time you know him but then you start noticing something about him, which would be how he never stops smiling all the time.
Kyouji has never be seen upset of sad, he never seems to show any emotion more deep than being nice, this does not means by itself that Kyouji is disturbed but if you compare him with Tetsuya, the other stoic character that never opens his eyes Kyouji lack of emoting becomes more apparent.
My theory would be that:
Kyouji is a Stepford Smiler: Its possible something happened in Kyouji past that greatly damaged his ability to feel (or maybe he was simply born that way), Kyouji fearing people wouldnt accept him this way started to practice smiling and do good deeds because he wanted to be accepted and he thought this was the only way people would like him.
Coaching and hanging around Soutarou is pretty much Kyouji way of helping somebody who he feels is similar to him, since Soutarou was likely, really lonely because he was not only the town new kid he also lacked a father. Soutarou and Kyouji most likely meet when Soutarou joined Soccer because he though it would be a great opportunity to make friends, this really didn't take off though and he started looking up to Kyouji.
Kyouji noticed how Soutarou wasn't so different to what he is and he let Soutarou be his friend because he felt it was the best way for Soutarou to not end like him, with the double benefit of having a real friendship for likely the first time ever.
- If this is true, then it would be one of the most heartwarming outcomes of the Stepford Smiler trope. It would also most certainly make Kyoji and Soutarou's route a One True Threesome.