I'm going to assume we're talking about corporeal immortality here, since spiritual immortality is a different question, I think. Reasons why someone might want to live forever:

Self-centeredness. If I am the most important thing in my world, then my continued existence is the most important thing I can achieve. Let weaker humans seek immortality through a legacy of art or works or family - I can achieve the genuine thing.

Control. I would hand on my business / my estate / whatever to my successors, but they can't be trusted to do as good a job with it as I would. Or, think of how much additional power I can amass if I have more time to scheme and strategize. (Nobody expects to be poor and immortal; they expect to be rich and powerful and immortal.)

Fear. I know what life looks like. I don't know what death or an afterlife may be like.

But yeah, I'm with you in thinking it would eventually become tedious, absent the Eternal Enemy to deal with. In Michelle Sagara's Elantra series, a nearly-immortal elf comments to Kaylin, the human main character, something like she has no understanding of bored elves get and how much they value something new and surprising.

Or, quoting Susan Ertz, "Millions long for immortality who don't know what to do with themselves on a rainy Sunday afternoon."