1. NFP (when used to avoid preganancy) involves some days of abstinence each menstrual cycle. While this first seems negative, they discovered a positive value. It became like a monthly renewal of engagement when they would express their affection by other means: holding hands, a hug, a walk together, a poem, a flower, etc. After that would come what was like a mini honeymoon. Thus NFP actually strengthened their affection.
2. It gave them greater confidence in each other. She knew that if he could exercise self-control during her fertile times, he was more likely to be able to do it when he was away from her. Also, when the wive is on the Pill, she is "available" to him at any time - but he also knows in the back of his mind that she is also potentially available to other men. Since the Pill was introduced in the 60's, infidelity has skyrocketed along with marital breakdown.
3. They are respecting the integrity of each others' bodies. Do you know any prescription - besides birth control - which is not aimed at helping the body to function normally? Birth control is not really medicine because it takes away a normal function of the body. The Pill, Depo Provera, Norplant, IUD, tubal ligation have one purpose - to render a young woman infertile.
4. Birth control can lead to what is called a "contraceptive mentality," that is, desiring such control that when a "failure" happens (only complete abstinence is 100% effective) the couple will more easily be tempted to abortion. A Guttmacher study showed that most of the women who obtained abortions were using birth control the previous month.
5. But even more serious, birth Control can involve not just preventing conception, but the destruction of tiny human lives. One of the mechanisms of chemical means is to weaken the endometrial lining of the uterus. If conception takes place the new human life cannot implant and thus dies and is expelled at the next menstruation. Birth control not only makes a couple more open to abortion, it is abortion. (The mechanisms I mentioned are no secret, altho doctors seldom explain them to their patients. For verification, check out the Planned Parenthood site's description of birth control methods.* See also: Blurring the Line)
6. Most important NFP does not destroy ones relationship with God. A Catholic who uses birth control is in an objective state of sin and is not eligible for communion until repenting and confessing the sin. To receive communion in that state does spiritual damage. (see I Cor 11:27ff) Up until very recently Protestants also considered birth control a serious sin. Martin Luther, the founder of Protestantism called it "worse than adultery or incest" (Commentary on Genesis 38:10).