She/he never lets me see the kids. Why do I have to pay child support?

The legal obligation to pay child support is completely separate from the issue of visitation rights. If you are court ordered to pay child support, you must do so regardless of when or if you see the children. If there is a court order giving you visitation and the custodial parent refuses to let you see the children, your recourse is to file a motion with the court asking that he/she be held in contempt of court.