There has been studies on this, being paired up with some kind of helping figure yields measurable outcomes, even if the person has no psychology training. Even religious mentors yield positive outcomes.
I think attachment, from attachment theory, explains part of this. When people are paired up with a helping figure, they may come to develop more positive mental representations of others. E.g. you have a good relationship with your coach, so your brain understands that this type of positive relationship is possible with other people. But this is mostly relevant for people who had an insecure attachment or had interpersonal problems. The other aspect of it is that two heads are better than one. People become entrenched in patterns of thinking and being, and without someone to provide correction or to show a different way of being, that person may not be fully conscious of what they're doing or aware they could be doing things differently. And I think people need an "expert" to tell them this. If your wife or a family member tells you off about a bad habit of yours, you're probably not going to listen. But a stranger, who you view as a expert in their field, tells you what you're doing is wrong - you're going to listen.