Every time I hear that argument, I picture something like this:
"Hi, I'm a human being"
"And I'm an AI"
"I can be happy, and sad, and any way in between"
"And I'm immortal"
"I can write music, and poetry, and I have a sense of humor"
"Still immortal here"
"That's nice, but I can do romance, burn with passion, suffer the pangs of despised love and all that"
"Right. Did I mention I'm immortal?"
"Yes, you did, and it's getting boring."
"Funny, because I never get bored. Which is a good thing because, you know, immortal"