Ah, so! I have the DVD, but I did not notice that. Evidently, in the context of the movie, the repetition of "you" makes sense. Thank you for pointing that out.

However, in the old MIT Outing Club songbook, from which I first learned this song about 1960, the second "you" is indeed changed to "I", and that is a good idea if one is singing the song in company rather than watching the movie. Likewise, the last two verses, which are topical in the movie, are left out.