Another question: What's the best translation of петушиться?

My FIRST guess was that it must have something to do with prison homosexuality!

But that obviously makes no sense in this context, so my second guess was "to strut proudly like a rooster" (referring to the boastful Americans). However, after Googling, I think that maybe "to have a hissy-fit" might be the intended meaning here (referring to Soviets who felt bad about losing the Moon race).