Nah, this isn't a great point at all.... even at face value really.
Put slightly differently, if we're assuming people sleep around as much as the text implies, if we focus on birth control solely for men, then one 'failure'/non-controlled man would result in a ton of pregnancies. If the onus is on women, then one 'failure'/non-controlled woman would result in one pregnancy.
Maybe, though she could also be a paid propagandist -- many of her posts have a certain bias to them. I'm honestly just curious, given the volume of posts she seems to make.