Whenever folks raise "false reporting" of rape as a concern, I mention that this occurs for sexual crimes at about the same rate as with other crimes such as theft, but because sexual assaults are so massively underreported the percentage is much, much lower. I also ask the questioner to think about "What would be in it for the woman"? We know rape very rarely goes to trial and when it does, less than 1% of cases end in a conviction. The criminal justice system is such that the burden of evidence is stacked against women when cases rely on "her word" and physical indicators are often construed as being unprovable as having occurred without consent.
But the clearest, most obvious reason can be deduced by looking at our own reactions, the reaction of those around us and the media, to see the way victims are treated. Even so called "good" victims, such as Nina Funnel . Nina was badly injured. This man nearly killed her, and still people suggested it "wasn't that bad" because he didn't actually penetrate her with his penis (because she fought him off). Speculation was blurted out about her wearing headphones, having a few drinks, walking home alone. Her article in the Daily Telegraph is a must read.
All of this - every single bit - contributes to more rapes. Women don't talk about sexual violence or aggression because when we do we're treated as pariahs. The community accepts rape not only as inevitable, but as in fact - sex. Think about that. Our understanding of sex includes men's violent domination of women's bodies.
When we participate in victim blaming, we actively engage in upholding the factors that ensure the continuation of violent misogyny. You know what would happen if we believed and supported women? Less rape. That is what would actually happen. We could, and can, end rape.