The Dunning-Kruger Effect basically states that unintelligent/unwise people of the not have the where with all to under that the fact that they are unintelligent/unwise. So what might be the relationship between this effect and Feminism? Think about it for a bit.
In today’s world, the Government has cleared a path for girls and women, and it did so at Feminism’s request. Women are subsidized more, given preference in hiring and promotion, and overall have their desires catered to. Men, on the other hand, have none of these advantages. Boys and young men are the most part not coddled. They are forced by this environment to develop themselves and to learn what is effective in the world and what isn’t. Ideally, they learn their limitations (often the hard way), and are therefore less likely to have an inflated self-assessment. As a white male, I know that I have to be better than others, and hence operate from a realistic view of the world.
None if this is true for modern young women. Due to their subsidized/coddled nature, they never actually are compelled to develop their intelligence/wisdom. This situation leads to fertile ground for the Dunning-Kruger Effect to fester and grow.
No doubt commenters can add their own evidence (anecdotal and otherwise) to this.