When Pope Paul VI wrote Humanae Vitae, he flabbergasted the world, especially parts of the Catholic world. Many expected him to signal a change to almost-two-thousand years of Catholic teaching regarding human sexuality, and when he didn't bend, he faced widespread rejection and ridicule.
Despite the reception, the encyclical itself is a beautiful presentation of the call of married couples to remain true to their vows and true to their natures. It's a sticky subject when we are culturally averse to permanent commitments and to conceding that we have inherent natures, and so for those for whom those are leaps too far, his encyclical may be of little interest. For those who think that natural law applies even now, and that wedding vows are not just empty words, this encyclical is eye-opening and beautiful!
(As an aside, Crystal asks Joseph for an analogy around the four-minute mark. He does provides it, but not until around the 20-minute mark, with a lot of intervening commentary in between.)
We hope you enjoy our discussion of it; it's just Crystal's favorite encyclical. It's also a relatively short work, so check it out if you have the time!
http://www.vatican.va/content/paul-vi/en/encyclicals/documents/hf_p-vi_enc_25071968_humanae-vitae.html