Sleep deprivation is a right killer, and turns pretty much anyone into an unpleasant, surly person you don’t want to be around. Me and my wife have never argued as much as we did that first month.
Post-natal depression is a real thing, too – might be worth checking.
Another thing is that everyone expects the mother to be perfect with kids, that somehow (by art of magic) she knows exactly what she’s doing with the newborn. This is a lie. She has no more idea about it than the father, there’s just a whole load more pressure on her. So it’s not just the general stress of a newborn, it’s even worse.