Here is what our US Bishops have written on the topic: (emphasis added)

"On the surface, there may seem to be little difference. But the end result is not the only thing that matters, and the way we get to that result may make an enormous moral difference. Some ways respect God's gifts to us while others do not. Couples who have practiced natural family planning after using contraception have experienced a profound difference in the meaning of their sexual intimacy.

When couples use contraception, either physical or chemical, they suppress their fertility, asserting that they alone have ultimate control over this power to create a new human life. With NFP, spouses respect God's design for life and love. They may choose to refrain from sexual union during the woman's fertile time, doing nothing to destroy the love-giving or life-giving meaning that is present. This is the difference between choosing to falsify the full marital language of the body and choosing at certain times not to speak that language.

The Church's support for NFP is not based on its being "natural" as opposed to artificial. Rather, NFP respects the God-given power to love a new human life into being even when we are not actively seeking to exercise that power. However, because NFP does not change the human body in any way, or upset its balance with the potentially harmful drugs or devices, people of other faiths or of no religious affiliation have also come to accept it from a desire to work in harmony with their bodies. They have also found that it leads couples to show greater attentiveness to and respect for each other.

"NFP has helped me mature, though I have a long way to go... It has caused me to cherish my wife rather than simply desire her." (Faithful to Each Other Forever, p45-46)" Married Love and the Gift of Life USCCB Nov. 2006 document)

NFP is using what God has built within us to be responsible parents. It allows couples to use their human wisdom in cooperation with God to build their families in a loving and responsible way. NFP teachers help read the language of the body. This is meant to teach the mystery of the person. It helps build a greater intimacy and true respect between the couple.

Making the choice to practice NFP had a profound effect on our lives. We began using NFP because we wanted to use something natural. We saw it as part of a healthier lifestyle. We didn't do it for any moral reasons, yet using NFP led us to God. We were also fortunate to begin home schooling and began to have contact with devout Catholics. We began to learn more about our faith. It's been a great journey and it all began with the decision to reject contraception. I'm sure people were praying for us.- Testimony from one of our couples

Birth Control and NFP

NFP accepts fertility as good and as integral to the person, rather than a disease to be suppressed. A couple who, for good reasons, refrain from intercourse during the wife's fertile periods do not falsify the language of the body by deliberately rejecting their potential fatherhood and motherhood. They either speak the language in truth through sexual union, or they find nonsexual means to express their mutual love. The language of the body is only spoken in truth. In the language of the body, the difference between NFP and contraception is the difference between refraining from speech for a time and lying. - Mary Healy, Men and Women are From Eden

The practice of periodic abstinence shapes the character of a couple, deepening their respect for one another as persons, strengthening their mutual love by fostering communication and non-genital forms of intimacy and thus helping them grow in chastity. In other words, rightly understood and used, NFP is not just another method of "birth control." It is a practice that builds virtue andenables a deeper and more authentic love. - Mary Healy

There is a fear of NFP because people think those who practice it tend to have more children. This would mean that the method doesn't work.  What is really at work here is that people practicing NFP become more generous, less selfish, and recognize what a true gift from God children are. The method “works” and does more for you and your family than “control” fertility. Children are a gift from God (articles 2373 to 2378 Catechism).