This is for health insurance, your taxes and also for your retirement pension. Being autonomo is a handicap, this is true, but you are your own boss, choose your working hours, clothes etc as you want, stop working "when you want" and are supposedly paid for extra hours, so not all is bad after all.

He's paying for a retirement pension, but not __his__ retirement pension.

Your final pension depends on what you have paid in your worker's life. So he's paying "for a promise of having a better retirement pension".

Which taxes?

I am a Spanish "autonomo" living in Germany: healthcare is way more expensive here in Germany (and in many ways lower quality). I see Spanish freelancers complain a lot about how expensive healthcare is for them, but when you compare it with the rest of Europe/USA, it is quite cheap I'd say.

Those 378 euros are not just for health care, but also for retirement.