Two reasons. One it needs to be economically viable for people to have and raise children. Otherwise they will not and society will collapse.

Two it is in any democratic societies best interest to have children be educated. And you being a part of society share this same interest. Alternatively we could take a very libertarian approach to education but the result is that you end up with a lot of bored youth who are of course a prime resource for anyone with profit or power motivated ideations to take advantage of.

If there is one socialist ideal that I am in favor of it's public education. Not to say our current system isn't deeply flawed and filled with problems, but a lot of that is because the schools reflect powerful interests rather than the interests of the society they serve at large.

But to put it in very simple terms. I'm happy to pay to have my poor black neighbors kids sent to school. Because in the event that their home life is fucked up beyond belief, that does give them a potential out. And ideally if the kids are in school learning how to make money then the less likely they'll see gangbanging as desirable future.

Now our schools fucking suck at this last point. But that's an issue with crappy schools and not schools inately.