There's a difference between "can make a better person" and "will make a better person".
Personally, I prefer to say it can help people become better people. The MA training doesn't do the work, the people do. And there's nothing magical about MA in this respect. As
@Steve has pointed out before, there are other activities that can help build the same traits. MA (or football, or tennis) can be hard work (if you train seriously in it), which builds discipline if people stick with it. Following rules for the benefit of others, showing respect for people who are helping you, etc. are all part of the package.
EDIT: And teaching about relationships is highly tangential to MA, so MA training is unlikely to be a big help in that area, other than helping people have better self-control.