First, I have to question the premise in a couple of ways. In the middle ages, literacy was not massively lower than in antiquity, because both lacked mass education and printing. Before large scale education and printing became possible, the overwhelming majority of people were non-literate agricultural workers. We simply don't hear their stories, because they were, of course, non-literate. Pre-Modern European history is more than anything written by the writers, who make up a particular class, which, while it varied in size, was always a small fraction of the population. Accurate statistics are impossible, but I would be extremely surprised if the literacy rates of any part of Europe much exceeded 5% or so in any year before about 1500. We do not, of course have any data.

Secondly, even among the elite, I don't have any reason to think that by the later middle ages literacy rates were substantially different than in antiquity, though in the early middle ages, they probably were, so let's talk a bit about why.

The short answer is economics: The Roman Empire was huge, and had, for its time, a tremendously large and coherent state, with a huge bureaucracy to run it. It had to. Keeping its armies paid, its buildings built, its walls maintained, its taxes collected, was a nigh impossible task for a pre-modern society on that scale, and it required a legion of clerks, lawyers and so on to make it happen. Further, that meant that the circles of power were, by definition, literate ones. If you were an elite, or wanted to be, you had to be literate, because everyone else was. For an example of this, I was just reading St. Augustine's confessions, and when he talks about his schooling, he makes it clear: he was taught grammar and rhetoric because it was seen as necessary for success.

When the Western Empire declined and fell, this bureaucracy slowly fell into decline as well. It wasn't immediate, nor complete, and indeed, many of the successor states in the west did their best to maintain Roman systems, but without a large state to administer, there simply was no economic justification for, nor way to pay for, a large cadre of educated people to run everything. If you were a small scale lord, you might only need, say, one guy, to go around collecting rents from your land, and you might just do it yourself. There's no need to pay a professional (even if one was available), a large amount of money (Remember, even in antiquity, the literate were the elite, paying for their labor wasn't cheap), in addition to paying for parchment, ink, quills, etc, all to keep detailed records, when you could probably just remember it all.

Even for the richest kings, the bureaucracy needed to administer their rather loose kingdoms was relatively small, and so there simply was no need for a substantial literate class. For years here, we're talking about maybe 600 AD-1000 AD, and I should add the addendum that this is entirely untrue for the eastern empire, which chugged on just fine for centuries after the fall of the west, and stayed plenty urban and plenty literate. After about 1000, for a lot of reasons, the medieval economy started to improve, crop yields and surpluses rose along with populations, kingdoms became more coherent, taxes began to be collected on large and formal scales again, and trade increased substantially. With all this, came a commensurate need for administrators, clerks, etc, and therefore the education system to produce those people. Universities start popping up to educate this new population in the late 12th and early 13th century, and then literacy was essentially on an upswing from there. The printing press represents a real shift, and the start of mass literacy, but the impetus for it was the rise of a substantial literate culture in Later Medieval Europe. The printing press was brought to Europe when it was partially because there was a market for its products. People wanted books, and the press made them much more affordable.