Sort of like how a lot of cops were crime victims, and a lot of doctors were sick kids, a lot of psychologists had their own problems, first.
None of that ^^^ is all first person. My friend was shot, my mom was sick, I didn't know how to help, is probably just as common.
But then you've also got 'Family Business' people; My dads a cop, my mom's a doctor, my favorite uncle is a psychologist... People they admired as kids/adults, and have been around that world because of them, their whole lives. And that's the world they want to belong to as adults.
(But wait, there's more!) Other people just sort of fall into a career with no background, personal or professional. Usually? They take a class in college and OMFG! This is amazing! Or they volunteer somewhere, and wow. Just wow. If I were going to do anything? It would be this / what they do. Or they work in a related field, and that field exposed them to the other one, and dayum. Cop <> Lawyer, secretary > cop/doctor/psychologist.
As far as any particular brand of crazy? LOL. Purely anecdotally, whatever field someone works in, in psych, there tends to be a bit of a history, there. Not always. Not even most of the time. Not every child psychologist who works with kids in divorce comes from a divorced home. Some people just really love kids, and that specialty (kids & families in transition) allows them to work with all kinds of kids. Other people specialize in certain types of kids (learning disabilities, abuse, giftedness, poverty, prolonged illness/injury, etc.). Just like not all rape counselors have been raped, and not all eating disorder therapists have an eating disorder. Shrug. But there is a bit of a tendency.