The author just stop justifying their points after the first couple. It is like they starting writing a really good piece, then got two "myths" in and then switched to random opinion mode.
However I've been to this rodeo before many times, and unfortunately if you get drawn into a discussion that is, at the foundation, based on personal opinion/perspective then you never get anywhere.
You need to try and stick to the science. When the study that the author used as their first point was published there was some great discussion that focused around the science of sexism.