I’ve seen the terms dogma and doctrine used inter-changeably. I think this is Okay, although technically there is probably a difference. Neither changes but they do undergo development, which is to say deeper understanding and definition.
The Church’s teaching on birth control is an infallible teaching. This teaching has been held universally in the Church since the time of the apostles. Moreover, all Christians held this belief until the Anglican Communion broke ranks in the 1930’s. Since then, only the Catholic Church has held firm.
Infallible teachings are those that have been held universally in the Church, or have been infallibly defined, or both. Even before Paul VI wrote Humane Vitae, there were Papal encyclicals that gave the same unaltered teaching. This has also been the teaching from the Magesterium. Because of these things, it is considered an infallible and unchangeable doctrine.
The truth of the doctrine becomes more clear when one studies the reasons for the teaching. The reasons are in themselves spiritual and moral truths. These are all consistent with the natural law. Check it all out. I think you will find it all quite persuasive.