Okay, let's say they change the laws and men can rebut the presumption of paternity. Great, we're moving forward to a future of men being able to enjoy the fullness of their rights.
But do you think you'll be allowed to refuse? Health-insurance companies have an interest in whether that child is yours, because he or she is going on your insurance policy. They have a fiduciary responsibility to other policyholders and shareholders to ensure that nobody gets paid for who doesn't belong, after all...and they're not paying for some stranger's child. You don't get to refuse, not if you want continuing coverage.
Now all paternity rights are in the hands of some lab tech who may or may not be helping himself to the contents of the medicine cabinet--or even more fun, some feminist lab tech who decided she doesn't like men for whatever reason.
Off to the family courts, to divorce that unfaithful
whore and sever your ties to her bastard child she tried to foist on you. You might even get her jailed for paternity fraud. She swears she's never been with anyone but you, but the evidence is there, incontrovertible! Let the
real father pay for his own kid--and if she never finds him, well, that's no concern of
yours. She can get welfare.
On the long odds that you find out the tech was a supreme fuckup, well...good luck reconciling with your now ex-wife, much less fixing all of it without bankrupting yourself in court proceedings (before a judge who already hates you for being male).
Over the top? Maybe. But then again, people do have a bad habit of ignoring the evidence of their eyes and their gut in favor of "scientific" proofs (no matter how easily forged, falsified, or corrupted they can be).