Just like the prohibitions against polygamy, slavery, and abortion, the ban against contraception is based primarily upon reason and natural law.
It's a church-made law by a (supposedly) celibate priesthood.
Historically, opposition to contraception wasn't just a Catholic phenomena. Every mainstream protestant denomination prohibited contraception until 1930 when the Anglicans decreed it to be morally permissible in only the most dire circumstances. Most protestant denominations continued their prohibitions well into the 1950's and 1960's.
Read Tamar's excellent analysis for why Scripture doesn't speak to the issue of contraception at all. If reason and natural law are the basis for this prohibition what do reason and natural law say about the perfectly reasonable decision not to expend ourselves as brood mares and impoverish ourselves trying to raise 12-14 children? Who has standing to tell us what sort of life we will make for ourselves and the children we choose to have? A celibate priest with no scriptural basis for his decision? I think not my friend. There is no natural law basis for the decision to waste ourselves physically or economically raising countless children we need not have and neither one's neighbor nor a priest has the right to even suggest the nature of the loving relationship a couple may have.