It's not that. The standard argument is SELF-ACCESSIBLE college gives people the ability to get jobs by allowing them to, on their own, by their own assessment, using their own resources (time at least; money, if doing student loans instead of government-paid college), obtain a marketable job skill.
In a market where students can reasonably self-propel (that is, where anyone not sufficiently rich can send themselves to college), the absolute best course of action for the individual is to go to college and get a degree. Further, the best course of action is to get the degree in whatever field appears to provide the best immediate employment opportunity. These are both direct manifestations of the Prisonner's Dilemma; the latter involves a massive amount of market analysis, much of which is blind and long, meaning a lot of uncontrollable risk.
In such a market, students primarily face the risk of other students trying to enter the same market. Students cannot readily project how many jobs will be available in a field, how the field will grow, or how many other students will gain credentials for that field. Because *not* studying in that field provides even *worse* results, students must simply accept these risks. This creates floods of labor in the market, dynamically, driving down labor costs by creating high unemployment and a reduction of labor power, all through the simple mechanism of making skilled workers an over-supplied and readily-interchangeable commodity.
Besides the bargaining power problem, I believe this is plainly inefficient as an overall market strategy. It's an expensive way to produce an effective workforce.
In a non-intervention college market (where the government focuses on K-12, but not career education), the great majority of individuals cannot send themselves to college. Businesses, thus, suffer from a lack of required skilled labor. This sharply impacts each employer's ability to execute business strategies, placing them at sharp disadvantage to any other business which can effectively execute their own strategies. It's incredibly painful and destructive to business.
In such a market, the best action for any business is to hire entry-level employees and train them. Entrants can, almost immediately, take over low-skill, time-intensive work. Even shit programmers can hunt down and identify bugs, clean up code, and so forth; these things take the most skilled programmers some time, sometimes even hours or days, and so letting your $40k worker grind it for a week or so instead of having your $100k senior software engineer spend five days trying to track it down is at least breaking even. Carpenters who can't make intricate carvings can at least build rough furniture; those who can't can plane floors; those whose skills are so poor can at least lay joists; and those who are too inexperienced and terrible to lay joists can, at least, spend the hours of the day cutting wedges and shims, tasks which are too time-consuming for an expensive artisan to waste his day on.
Businesses in this context have stronger (still imperfect) insight into their individual needs, their market growth, their departmental expansion, and so forth. Often during times of expansion we approve budget 2-3 years in advance of hiring new accountants, programmers, sales people, digital artists, and master control engineers; during normal times, we approve budget 6-12 months in advance, when the need is recognized on the horizon. No student can so accurately and consistently project that there is a job somewhere out there waiting for him after college.
This arrangement is undesirable to businesses, as it makes workers valuable (this is a lay-term, not an economics one; the term "value" must be ejected from economic theory, while the term "valuation" must remain for market economics). Valuable workers are problematic: you can't just fire them and hire another interchangeable part. Workers, in an economic sense, have an up-front cost and a continuous cost, which become part of the cost of whatever product they produce; to fire a worker and hire a new entrant, you must now invest the up-front cost into the worker again, increasing the cost of whatever they produce. Such displaced workers save the up-front cost to the next employer, and may command an increased price if an employer needs a more senior developer and cannot wait to train a new laborer.
That means workers gain bargaining power and, ultimately, job security and stable salaries. On one hand, this raises their wage, which raises labor costs, which makes the economy less wealthy; on the other, this avoids a lot of poorly-invested expense in unnecessary college education, training laborers as needed rather than as a constant, freeing up a lot of capital (money) in the consumer's hands to spend on other things, creating new markets to obtain that residual wealth by selling the consumer new things, thus creating new jobs to produce those new goods and services, in all increasing total wealth.
As I said, our current strategy is inefficient. Considering 74% of STEM degree holders don't have STEM-related jobs and half of engineers don't work in engineering, there's a lot more waste than just liberal arts degrees.