Please forgive me if I get some chronology and names a tad mixed up. It’s difficult to review one’s texts from work.
I’d have to say that Lizzie was pretty well backed into a corner at that point.
She was facing a heap of pressure from the other nations, particularly the Pope and Spain, who’d figured by having Philip shack up with Mary (soeur), they’d get themselves a piece of the English pie and the first blow in a Roman Catholic reformation of Protestant nations.
Elizabeth was looking at criticism from several fronts. Roman Catholics who’d enjoyed renewed power under Mary I; Puritans who’d wouldn’t be happy until nobody was having any fun; nobles who saw their power slipping through their fingers as Elizabeth showed herself to be more and more self-reliant. Even her legitimacy to the throne was called into question by those who felt the only marriage of Henry VIII that counted was his first.
England had not had a strong monarch since Harry and Elizabeth was determined to rule by herself and for herself, without being beholden to stronger nations or rulers. She was a threat, and she had to make sure people knew that she was there to stay.
Mary, on the other hand, had an unassailable claim to the throne (through Henry VIII’s sister Margaret). She was a good Roman Catholic, and had every reason to dislike the Protestants. They had, after all, killed her husband, stolen her son, and kicked her out of her own country.
Furthermore, she’d been a pawn in someone else’s game her whole life. Raised in the French Court, she was sheltered from 6 years old to the day she was married. She had the bloodline, the religion, and the malleability the Roman Catholics needed.
Elizabeth forgave her as often as was politically safe. She’d shut down several plots “led” by Mary and did nothing but lock her up. The last one (Northumberland?) was the breaking point. Again, Mary was led by her nose by a scheming “lover” into planning Elizabeth’s overthrow and Elizabeth found that it was safer to have her executed than keeping her around.
Elizabeth was having enough trouble dealing with internal problems, and did not need pressure from the rest of Europe. England had not been a stable country since Henry’s time, and Elizabeth needed to establish and maintain her power base. Mary was threatening that base.
Mary was more than just another claimant to the throne. She was a legitimate threat that had to be removed. Forgiveness on Elizabeth’s part had done nothing. Her back was to the wall, and the only option left at this point was (IMHO), execution.