How is it misogyny? She's used as leverage to start the war, not "Hey guys look we hate/mistrust women".
well, the usual banter about dropping in for a date and saving the miss and stuff.
It's just hollywood action script writing, it can be expected but not excused if you want to look at it from that perspective.
Edited:
Haven't seen anything misogynystic in said dialogue.
But that's probably because I couldn't hear it over the sound of everything going to hell, like it always is in CoD. But I can expect soldiers, - on a battlefield, - to call names and be somewhat disrespectful towards just about anyone. There's no misogyny anyway. Disrespect to said woman, yes, maybe. Since when disrespecting particular woman, or, in this case, woman-looking-imaginary-characther is misogynystic?
again, I'm using the term misogyny in the most blanket way where yes, disrespect towards one woman can be equated to that.