I was doing grammar exercise, I don't understand why should I use must have been rather than could have been, is it because he suffered from a Long illness and he'll die anyway, so I should put must here? Can someone help me with it I'm kind of confused.
You are correct, there is nothing grammatically wrong with "could have", but the meaning is different. When you say "could have", you are talking about something that is possible, but not necessarily true. When you say "must have", you are talking about something that is true. Arthur Rodway must have been going through a painful illness. But while he was going through a painful illness, he could have also been going through other things, related or unrelated.