Why would someone openly say that they oppose human rights?

I doubt anyone you are talking to is opposed to all human rights, that sounds very much like a straw man statement. Reasonable people can disagree about whether any particular right should be protected by law.

The reason is simple: any legally-protected right you have stands in direct opposition to some other right that I could have:

• Your right to free speech is necessarily limited by my right to, among other things, freedom from slander/libel, right to a fair trial, right to free and fair elections, right to not be defrauded, etc.
• Your right to bodily autonomy can conflict with my right to health and safety when there is a global pandemic spreading and you refuse vaccination.
• Your property rights are curtailed by rules against environmental harm, discrimination, insider trading, etc.

No right is ever meant to be or can be absolute, and not all good government policy is based on rights. Turning a policy argument into one about human rights is not generally going to win the other person over, it's akin to calling someone a racist because of their position on affirmative action. There's no rational discussion that can be had after that point.