Why do Norman and Madge argue in the ending scene?

In the play The Dresser, by Ronald Harwood, Norman is Sir's dresser, protector, and confidant. Sir is one of the last actor/managers of an English regional touring theatre company, and he's spent his life performing Shakespeare.
At one time, Norman was an actor himself. He was taken under Sir's wing about fifteen years ago, and spent the rest of his career in Sir's service. After a lifetime of performing, Sir now suffers from very poor mental and physical health and requires near constant attention from Norman.
Madge has been the stage manager for Sir's acting company for over twenty years, and she has a longstanding, unrequited love for and devotion to him. She might have had a short fling with Sir when they were both much younger, but now she must simply stand back and watch the younger actresses come and go through the company.
Norman and Madge are much more alike than either of them realizes or will admit. Nevertheless, they frequently find themselves at odds with one another over their care of Sir.
For example, Madge believes that Sir should be committed to a mental institution, but Norman argues on Sir's behalf, telling her that taking Sir off the stage would kill him.
When Sir can't remember which play he's performing and can't remember his lines once he's told, Madge argues that he shouldn't perform the play, but she's overruled by Norman, and Sir somehow manages to makes it through the performance.
Back in the dressing room after the performance, Sir quietly dies. Norman and Madge are devastated by his death. Norman reacts with resentment and anger, however, while Madge reacts with compassion and resignation. Their last argument in the play is about Madge's reaction to Norman's selfish and less-than-kind reaction to Sir's death.
"What's to happen to me?" laments Norman. "What am I going to do?"
Madge responds quietly, "You can speak well of him."
In the end, though, they're really only arguing about how much they both loved Sir.