The phrase "כל הקרב הקרב כי לא לחנם הלך זרזיר אצל עורב" is found in a couple places in Shas (Chullin 65a, Bava Kamma 92b) and can literally be translated as:
not for naught that the zarzir went to dwell with the crow, but because it is of the same species
ie- birds of a feather flock together.
It's very easy to see how this can be construed as sexist, misogynistic, and demeaning- "we're going to learn Shabbos laws about animals followed by women since 'birds of a feather flock together?!'"
This seems outrageous!
I think it has a more innocent meaning. Namely, it's comparing animals and women because we're learning Shabbos laws that pertain to one's household. Animals, women, kids, one's elder paents possessions- all these are part of one's household. So the verse can understood as: "since we discussed one area of the household, lets discuss another area of the household."
While it may be misconstrued (and may not make for the greatest line in today's climate) I think this line was said lightheartedly and not intending to offend.