Because society has an interest in a large, well-educated labour pool that its entrepreneurs and companies can draw from. They can then employ these people, and pay them high salaries, a part of which goes back to education, and there you have a positive spiral.
Second, college is a good cut of because it's highly specialized education.
Third, almost all the benefits are captured by the precipitant of the education.
Finally, most of the country would either be unsuited or uninterested in college education. To a person breaking their back doing roofting, they might as well be buying rich kids trips to Europe instead. Not only does free college only benefit a portion of society, it benefits a portion that doesn't need a subsidy.
Scientific and technical knowledge drives innovation. Economic growth on a per-capita basis is entirely driven by innovation. Thus scientific and technical education directly impacts your quality of life.
With regards to liberal arts education, I'm inclined to agree that government subsidies may not be the best use of tax money.
Who do you think will start going to college more once it's free? Students who are driven to get a STEM career are already pursuing college. Making it free will attract the people who think along the lines of "I don't wanna start working yet, might as well go live the college lifestyle for free and get a sociology degree before I end up as a barista anyway." (I'm exaggerating slightly but you get the idea).
To be fair, I'm not totally against (at least partially) funding certain liberal arts degrees either. Specifically, creative writing and journalism are both valuable. For example, it would be profitable to subsidize many thousands of creative writing students to produce more popular writers like J.K. Rowling or Stephen King. Total yearly sales of fiction books in the US is ~14 billion, taxes from that could cover subsidies for creative writing if they were merit based.
College / university is specialized knowledge that is typically used for career and social status advancement. Its helpful and has utility, but it's not necessarily required to be a functioning adult that lives in and contributes to society
Paying for tution with tax money doesn't make it free. If you aren't willing to invest in yourself, why should society do so?
Free college tuition is a waste of resources on the upper middle class.