Free education means free as in price, not as in freedom. It is also understood by almost anyone who suggest it to not be free to society at large, but free to the person receiving it and paid for by society at large, same for health. At the level of a society, it makes sense because you want to live in a more educated capable society, which increases your own opportunities and standard of living regardless of what you do, given that society is interconnected. At the most individualistic level, you can consider the benefits to yourself of receiving free education when you are young, then paying for it in the form of taxes over the future and realize that public institutions tend to work better for this case than for profit loans in most cases.
Regarding the whole freedom from coercion argument. My question would be: isn't private property itself essentially enforced by government coercion? How is the freedom to not pay taxes any more sacred than the freedom to not being stopped by police if I steal from someone else?
Taxation is constitutive of the concept of a modern state. Now, we can discuss the pro's and con's of specific programs, the amount of taxation needed to fund them, how progressive such taxation needs to be and whether the benefits are worth the costs. I can say that I think socialized education is definitely worth it, and you can tell me that you don't believe it is, and tax policy results from democratic compromise among many such points of view. But the whole "taxation is morally wrong because it implies state coercion" argument is absurd, private property implies state coercion too and I have seen few libertarians suggest it should go away (in that sense, I believe full-on Anarchists have a more self-consistent view, even if I still don't agree with it).