"Why do some people oppose policies that favor women?"
I can't speak for everyone, but I oppose any policy that favors one gender over the other because I believe in equality. In most things, that is what I believe...but when it comes to state assistance, I believe citizens should be favored over non-citizens!
"Don’t they know these policies are needed to create a level playing field to give women a fighting chance to succeed?"
Well if I believed that to be true at one point, now we are seeing a situation where men are falling behind largely as a result of these kinds of biased female-centric policies.
Even if I agreed with you that women at one point needed the favoritism in order to succeed, we are well past that point now!
"I know I wouldn’t have gotten my current job if not for affirmative action."
So then you should understand when, in education, a good chunk of female teachers are fired and replaced with male teachers while women in post secondary studies are required to obtain higher marks to get in to university relative to their male counterparts.
Or is your point that favoritism in policies is only acceptable when it benefits you personally?