Should a man have to pay child support even if he never sees the child and another man considers him dad and gets him every other weekend and on holidays

Courts usually order that the biological father pay, when a mother petitions for support, unless the child has been adopted.
'Never seeing the child' is another matter. The bio father can ask for visitation, or to share custody. But not bothering to do that doesn't mean he doesn't have to pay support, and another father figure in the picture isn't relevant.

Yes, it is not the child's fault the father chooses not to visit. And it is not a matter of right or wrong, in the "right" world, the father visits every week and has a working relationship with mother.

In a "right" world, there is no need of a court order and the father gladly pays more than needed to help with his child

The biological or legal father is responsible for financially supporting his child. That's the law everywhere. Whether the father chooses to be a part of his child's life is immaterial.

So is whether another person acts as the father. Unless that person adopts the child and becomes their legal parent it does not relieve the bio father of their obligation.