I wasn't quite sure what to make of "If a man accidentally conceives a child with a woman...". I'm aware that in some cases a sperm donor has been forced to pay child support and I suppose there could be ways a man could unknowingly father a child but the article seem to imply cases where the father willing had sex but for some reason thought there wouldn't be a pregnancy.

There's just not a subtle way to put except that when a man has sex with a woman there is always the possibility of pregnancy. Condoms break, the pill is not 100% effective, vasectomies sometimes fail.

That's not to say there aren't problems with how paternity is treated in our current legal system. I just don't think downplaying the responsibilities men face is a good strategy here.