Higher education in the United States is increasingly expensive, leaving students with thousands of dollars in debt. Since higher education is becoming an essential part of getting a decent job, most people are unable to simply avoid going to college and racking up the debt. Many other countries have free or very cheap post-secondary education available to citizens, and the United States should follow suit.
In this day and age, a person typically can not advance particularly far without a post-high school degree or certification. For this reason, higher education of different types really is no longer optional. Providing people with equal opportunities necessitates ready access to higher education. This type of access is only possible through a program that permits higher education at no cost.
Education is only higher education if it raises your education above your peers. If everybody was able to attend college, then soon the college degree wouldn't mean anything. We already see the value of college diplomas dropping as more and more students go to college after high school. The solution is to actually start teaching people things they need before high school graduation, not to tack on another four years of sub-standard education to the end of the schooling.
No, higher education should not be free to everyone because individuals tend to place more value on things that have a financial cost. Students who pay at least something toward their education are more likely to work hard and stick with their program of study. Things that come freely are easy to take for granted or throw away.