If I may, I would like to finish the sentences:
"You spread the costs around and it'll cost less for the people who need it", and more for the people who don't need it.
"If you only make women pay for, say, birth control or pregnancy needs, you're shifting the costs on to women, making healthcare more expensive" ... for those who actually need those things (women), and less expensive for those who don't (guys). You don't increase health care costs overall, you simply distribute them differently.
Again, I'm not necessarily saying this is how it should be; I'm merely saying, the line of reasoning is not consistent with the blog.
Either you chose to ignore physical (dis-)advantages and spread costs evenly. In that case, guys pay the same amount for insurances & pension (my example), and girls pay their equal share in contraception (the blog post).
Or, you try to make up for physical disadvantages by giving financial advantages. In that case, men would have to pay less for their pension schemes etc., while girls' contraception would be subsidized. Saying the latter should be done, while not applying that reasoning to insurances, pension and everything else, is neither fair nor consistent.
"You should read up on how healthcare costs work."
I would love to, but that article doesn't exactly support your line of reasoning. In fact, it explicitly states
"Before Obamacare, it made sense actuarially for insurers to charge women more than men for coverage on the individual market."
The whole rest of the article is based on the argument of solidarity, which I have explicitly mentioned in my first post and which I have repeated in this one. This is essentially the first way of doing this: Ignore physical differences, and split costs evenly. Which also means: Split costs for contraception evenly.