The author fails to mention what is probably the largest downside to sex: an entire half of the population is completely unable to reproduce. The question "why do we have sex?" could be restated as "why do males exist?"
Unfortunately the answers to that question trouble some people so it's difficult to establish the truth. The simple answer comes down to the fact that a species has to find a balance between maintaining genetic diversity, which is important for resilience and adaptation, and maintaining a strong breeding population. Males are there to allow some really wacky variations to exist that just wouldn't be viable in females. It only takes a tiny handful of males to take part in reproduction, but it takes essentially all females (especially considering they are only 50% of the population to begin with).