In 1967 Pope Paul VI released encyclical called
Humanae Vitae. The document upheld the perennial (and traditionally Christian) teaching that contraception was contrary to the moral law. However, the same document goes on to endorse "natural means" of postponing the conception of children.
Humanity has long known that a woman's menstrual cycle has spaces of fertility and infertility. Couples have used this fact to space out children by not having sex during the fertile periods.
In the past this was done through the "Rhythm Method". It relied on averages and personal menstrual history to guess where a woman is in her cycle. Its usefulness and reliability have well-known limitations.
A more modern method is called Natural Family Planning (NFP). It also uses abstinence during fertile periods, but relies on various biometric markers to identify signs of a woman’s fertility. This method is far less dependent on a woman's regularity and – (when practiced rigorously) - achieves levels of certainty equivalent to modern forms of contraception.
And again, this method is approved by the Catholic Church.
Some people see the Church’s approval of NFP as arbitrary and inconsistent. They will commonly object:
“When non-Catholics want to have sex without having a baby, they use contraception. When Catholics want to have sex without having a baby they use natural family planning. It’s the exact same thing.”
Well... is it?