This is why we need to push for mandatory DNA paternity testing at birth. Men should then have the option to leave the marriage at *that* point without child support, because there is no meaningful "bond" yet between the male and the child at that point.
The women's groups are against this, but have not articulated a reasonable reason to be against it. The most that I've heard is that "all that does is tell you whether the husband is the father, it doesn't tell you who the father is". Yes, but that is precisely the point. If the husband is not the father, the husband has the right to know that, and leave without financial recourse. If he is aware of the child's other parentage based on the test, and elects to raise the child as his own, then he could be reasonably held liable for child support later on.
The only reason women are against mandatory DNA paternity testing is because they know that a certain % of women will have their children disowned by their husbands and will be financially in a bad place. Well my answer to that is: boo hoo. Think about that before getting pregnant by someone other than your husband.