Why couldn't medieval men or women read?

Schooling was only available to the wealthy, and the Church found it in their interests to keep the masses ignorant, so failed to fill the void. Even today, the Catholic Church does not encourage the people to read and study their Bibles - rather they prefer them to listen to the priest's sermons and do as he tells them.

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Many medieval men and women could read.

In some parts of Europe, notably the Byzantine Empire, most people were literate. The Byzantine Empire had a system of primary schools that operated at the village level; it was founded in 425 AD and remained in place until 1453.

There were also secular schools in other parts of Europe. Charlemagne founded schools and intended education in the vernacular so people could read in languages other than Latin. King Alfred the Great of England did the same thing. There were also schools in the High Middle Ages and Late Middle Ages that were specifically designed to prepare children of both sexes for business; these were called abacus schools.