I think what some people don't understand is that not rushing to convict a person =/= not believing the person.
If someone makes an accusation, the accusation should be investigated before the accused is punished. The problem with accusations of physical abuse, especially sexual abuse, is that the accusation is typically enough to taint people forever even if they are exonerated.
It's not just about women lying. A lot of time, there is just missing context. Like a woman can get drunk with a man, have sex with him, wake up and not remember anything, and accuse him of rape. Technically, even if they both were drinking together, a rape charge could be brought against the guy. Now maybe the case fizzles out, but his life could still be ruined and in that particular scenario, he didn't do anything that the woman accusing him didn't do. Situations like that are not as rare as some are implying.