Here's the reason not believing a rape victim is misogynistic:
In most cases that don't make it to court, the unprovable factor is consent. It's not usually that difficult to establish that sex has taken place, the question is 'did she consent to it?'
Now if she says she didn't, and he says she did, you have to ask yourself why she would lie if she'd enjoyed sex perfectly happly at the time.
Drunk? The law is pretty clear on that one - if you're drunk, you're incapable of consent. Anyone who has sex drunk is taking that risk. It's on your own head. And yes, not all drunk sex is rape, of course it isn't, but you risk-assess. And certainly in the context of a woman you've met at a club that night or a very new relationship, why would you take that risk? Because as well as the risk of being falsely labelled a rapist, you run the risk of actually being one and causing a woman huge amounts of distress. The vast majority of women who have what they see as consensual drunken sex they regret the next day, do not report that as rape.
Vindictive? To what end? Are we saying that women are inherently vindictive? How many women are likely to put themselves through the ordeal of an intimate examination and court, where their sexual history is paraded and they are cross examined, purely to 'get back' at someone?
A rapist has an inherent reason to lie - he has done something wrong and by denying it he may get away with it. A woman who claims she has been raped only has a reason to lie if she hasn't been raped. So by saying we should believe men and women equally, we are basically saying that women lie much more often than men.
And that's why it's misogynistic.