Feminism is built on believing women’s accounts of sexual use and abuse by men.

...said Catharine MacKinnon. This article gives us some numbers on false reporting:

Advocacy literature typically claims that about 2 percent of rape complaints are found to be false, the same rate as for reports of other violent crimes. But that figure seems to have no basis in research. According to the FBI, about 9 percent of rape reports are dismissed as “unfounded,” without charges being filed. While advocates claim that this is often because the authorities lack proof or distrust reports of acquaintance rape, dismissals due to insufficient evidence usually occur further down the pipeline. Generally, an “unfounded” complaint is one in which the accuser recants or her story is contradicted by available evidence.

Gauging the true prevalence of false accusations is extremely difficult, particularly since rape reports are handled and recorded differently from one jurisdiction to another. But what reliable information is available suggests that the figure is not insubstantial.

In a particularly controversial study published in 1994, now-retired Purdue University sociologist Eugene Kanin found that 40 percent of rape reports filed in an Indiana town over a 10-year period turned out to be false by the “victim’s” own admission. Kanin (ironically, a pioneering researcher on sexual assault in dating situations) has been widely criticized for using data from a police department that subjected rape complainants to lie detector tests, which many believe are likely to mislabel anxious or agitated victims as liars and pressure them to recant. He found a similar pattern, however, in police records from two state universities where lie detectors were not used and all victims were interviewed by female officers.

While Kanin has cautioned against generalizing from his research, his conclusion that “false rape accusations are not uncommon” is supported by other evidence. Some years ago, a Washington Post investigation in Virginia and Maryland found that nearly one in four rape reports in 1990-91 were rejected as unfounded, and many of the women in those cases admitted they had lied when the newspaper contacted them. In several surveys of prosecutors and law enforcement officials, estimates of the share of rape complaints that turn out to be false have ranged from one in eight to one in five.

Also there is this study:

Over 15% of the respondents personally knew someone who has been falsely accused
81% of the falsely accused persons were male
Nearly 70% of the accusers were female
In over a quarter of the cases – 26% – the accusation was made as part of a child custody dispute
11% of respondents said they themselves had been falsely accused of abuse

Those numbers have to be taken with a grain of salt though...