Only thing congenital I know of are the green and purple heart icon traits. However, the tutor is very important. Your tutor has a high chance of passing on his education, and also, if your stats are generally high, when your student gets an education event, they get extra stats from them. For example, a high martial tutor who teaches the student to be brave will also impart 1 martial. Checking the event file, the tutor needs at least a 10 in the relevant stat.