For some people, having a baby in itself can lead to not coping, e.g. post partum psychosis. "You just cope" isn't always true and not coping isn't necessarily a failure by the mother - no more than if she had cancer or a superbug and therefore couldn't cope.
But there are also other factors - abusive relationships, poverty, lack of support, overwhelming other responsibilities etc. that mean a baby could tip the balance and be too much for you.
I found having children brought a lot to the surface from my own abusive childhood. With my first baby, a boy, I "coped" OK though I was very anxious. My second was a girl and the effect was much worse - I expect because I was a girl myself and it just hit home how badly I had been treated. My anxiety became worse and I've been on meds for a while and had therapy. I cope well now, but without the help I wouldn't.
Because I'm from an extremely dysfunctional family, and DP's aren't much better, I've never had family support either. I think that makes a huge difference. If you are struggling or need a break and you can call on nice, responsible GPs or relatives to have your DC overnight, it must really help.