Why did Pip say Abel Magwitch is "my convict"?

In the classic novel Great Expectations, the main character Pip is given a large amount of money by an anonymous benefactor, specifically so that he can be "brought up as a gentleman" with "great expectations." While he hopes that this benefactor may be Miss Havisham, it turns out to be Abel Magwitch, a convicted criminal.
In fact, Magwitch is the very same convict that a much younger Pip helped out at the very start of the book. Right after his escape from prison, Pip snuck Magwitch food and a file to cut off the iron on his leg. Though Magwitch did at first threaten to kill Pip if he didn't help him, he was very grateful to be saved from starvation and saw a bit of himself in the boy. Pip comes to realize that Magwitch, while very rough around the edges, is not truly a bad person. Because of their shared history, and because he begins to care about Magwitch, Pip starts referring to him as "my convict."