Female readers tend to be more hostile to female protagonists than male readers are to male protagonists. Women tend to judge other women more harshly than men, and the main character of a book is practically set up to be judged.
Hopefully without going too far off-topic, have you an explanation for why this is, or perhaps a link to one?
There is a lot of material available on the topic of why women are critical of each other:
To sum up though: Historically women have been valued by men for their bodies and bodily properties such as youth, and women have been valued by other women for their behavior, while their appearances, political power, wealth, etc are a strong source of jealousy for other women. By contrast men have more often been valued for their performance and achievements, as well as their possessions. Women might be jealous of men's social freedoms or power and wealth, but men and women aren't usually in direct competition with each other; it's rare for anyone to be intensely jealous of someone of the opposite gender (though transgender or gay individuals might be in more direct competition with the opposite sex or each other and intense jealousies may occur there.) To me the interesting side of the question is why men aren't more often jealous or critical of male protagonists. There are certainly men who prefer female characters (e.g. the adult male bronies who love the almost entirely female cast of My Little Pony) but that's probably 30% or less of male audiences. In studies of erotica preferences, there is a noticeable percentage of both straight men and straight women who reject seeing their own gender in erotic situations due to some mix of jealousy and repulsion. But women seem to experience this with non-sexual fiction as well, while men don't as much.