I thought that at one time too. But listen to the other side of the argument which is based entirely on the natural law. Note this prophetic passage in particular.
Responsible men can become more deeply convinced of the truth of [this] ...if they reflect on the consequences of methods and plans for artificial birth control. Let them first consider how easily this course of action could open wide the way for marital infidelity and a general lowering of moral standards. Not much experience is needed to be fully aware of human weakness and to understand that human beings—and especially the young, who are so exposed to temptation—need incentives to keep the moral law, and it is an evil thing to make it easy for them to break that law. Another effect that gives cause for alarm is that a man who grows accustomed to the use of contraceptive methods may forget the reverence due to a woman, and, disregarding her physical and emotional equilibrium, reduce her to being a mere instrument for the satisfaction of his own desires, no longer considering her as his partner whom he should surround with care and affection.Keep in mind that all Protestant denominations opposed artificial means of contraception until 1929.
That is a derivative argument and awful shaky ground to set up a prohibition. By that logic, one could ban cars because of the temptation to speed, especially for the young.
I'll ask you the same question. What Bible verse prohibits contraception?