If the goal of natural family planning is to avoid pregnancy and the goal of contraception is to avoid pregnancy, why is one approved by the Church and the other is not?
A determined goal can usually be achieved in multiple ways. I can stop you from walking across my lawn by asking you to stop, putting up a fence, calling the police, etc. or I could break your legs. The end result is the same, however how it is achieved is quite different. Just because two courses of action have similar results does not mean the two courses of action are morally equivalent.
When it comes to natural family planning v. contraception they are different means of achieving a determined goal. In NFP the couple essentially just abstains during the fertile periods. They are abstaining from doing something. No one is obligated to have sexual relations at any one particular point. They therefore are doing nothing wrong.
When couples use contraception they are acting in a manner that removes the procreative aspect from the marital act. They cross the line from refraining from performing an action to performing an action that prevents the procreative aspect of the martial act from being present.
When engaged in NFP couples are fully aware of the procreative aspect of human sexuality and act (and refrain from action) in a manner that is respectful of God’s gift of sexuality. When using contraceptives couples act directly against the procreative aspect of the marital act as if its an evil (which it is not).
Of course, even those who use contraceptives know there is a definitive difference between NFP and contraception. If NFP and contraception were completely equivalent, as they sometimes claim, then users of contraception should have no problem switching to NFP…