Why was Thomas More canonized?

Quite simply, because he fulfilled the requirements of canonization, described here.

It appears that the main reason for them opening the canonization proceedings for More was his martyrdom:

More was beatified by Pope Leo XIII in 1886, along with other English martyrs, and canonized in 1935. Had he never met death for the faith he still would have been a candidate for canonization as a confessor. From first to last his life was singularly pure, lived in the spirit of his own prayer: "Give me, good Lord, a longing to be with Thee; not for the avoiding of the calamities of this wicked world, nor so much for the avoiding the pains of purgatory, nor the pains of Hell neither, nor so much for the attaining of the joys of Heaven in respect of mine own commodity, as even for a very love of Thee."

Source: St. Thomas More.

One reason could be because he was "martyred":

he steadfastly refused to take the oath of supremacy of the Crown in the relationship between the Kingdom and the Church in England. Holding fast to the ancient teaching of Papal supremacy, More refused to take the oath and furthermore publicly refused to uphold Henry's annulment from Catherine. John Fisher, Bishop of Rochester, refused the oath along with More. The oath reads:

...By reason whereof the Bishop of Rome and See Apostolic, contrary to the great and inviolable grants of jurisdictions given by God immediately to emperors, kings and princes in succession to their heirs, hath presumed in times past to invest who should please them to inherit in other men's kingdoms and dominions, which thing we your most humble subjects, both spiritual and temporal, do most abhor and detest;

Because of this, he was then charged with high treason, and was convicted, and consequently, decapitated. I suppose, the Catholics believed this to be "martyrdom" as More stood for his beliefs rather than compromise, even on pain of death, and so, they canonized him. That, is a possible reason.

Edit: This is not the sole reason he was canonized. This, can be combined with the fact that he had great reputation:

The steadfastness and courage with which More held on to his religious convictions in the face of ruin and death and the dignity with which he conducted himself during his imprisonment, trial, and execution, contributed much to More's posthumous reputation, particularly among Catholics.

Catholics argue that More was not guilty of the torture that he was accused of.

In this article, scroll down to the "Smear Campaign" section that speaks about it.

My understanding is that most of the surviving historical records of the time, were written by More's enemies (and executioners) who would have been very much slanted in their accounts, dubious at best. And that the records that indicate that he killed and tortured in the name of the church were only recorded by a handful people.

With the entire political system being turned on it's head by Henry at that time, there would have been plenty of motive to falsely accuse someone seen as a martyr for the opposing side.

There are two additional reasons for More's canonization. The first reason is that the Vatican wished to support English Roman Catholics over against the Church of England. Anglican-RC relations at this time were very frosty; and because More had defended papal (as against royal) supremacy in the church, and died for his conviction, he qualified as a martyr.

The second reason had to do with the times. In 1935, when More was canonized, Hitler had been in power for two years. More, in this context, was a great example of a layman standing up for his faith and resisting tyranny. It was a way of encouraging German Catholics to do the same.