Why were English and Scottish Protestants being persecuted during the reign of Queen Mary I?

Mary I wanted to crush the English and Scottish Protestants both to fully legitimize her rule and for personal reasons.
Mary grew up in one of the most tumultuous periods of English history and suffered as "collateral damage" as a result. Her father, King Henry VIII, decided that he had never been married to her mother, Katherine of Aragon, in the eyes of God. Henry VIII felt this way because Katherine had not borne him a male heir. He believed the lack of a male heir was God's way of punishing him for his marrying his brother's widow, a sin according to Old Testament law. (Katherine of Aragon had for a short time been married to Henry's older brother Arthur, who died young.)
Henry also, incidentally, fell deeply in love with another woman, Anne Boleyn. He shattered England's relationship with the Roman Catholic Church when he took England out of it in order to facilitate marrying Anne. He declared himself the head of the English church, got his divorce without papal approval, and married his beloved. As a result of all of this, England became a Protestant country, and Mary was declared illegitimate.
When she became queen on the death of her brother Edward, Mary moved to bring England back into the Catholic fold. This was important politically, because as long as England remained Protestant, she could be accused of being illegitimate and therefore without a strong claim on the throne. Beyond that, she understandably had many bitter feelings about the way she and her mother had been treated and a strong belief in Roman Catholicism.
As a result of both political necessity and personal conviction, Mary vigorously persecuted Protestants, wanting to stamp out this, to her, upstart branch of Christianity and reinstate Catholicism as the religion of the land.