Try to imagine it as Neelix is your brother-in-law - the brother-in-law that you can't stand. You dread any thought of having to share a day with this guy. But there are times when, say, there's a huge party or something and you can spend time with other people, and you only see him for a few minutes at a time, and during those times he's not acting like a complete twerp. And you can admit "Okay, well, he's not completely without any redeeming qualities," right?
And then one day, one day comes along and you're told "oh no, haven't you heard? He's got a terminal disease. He is not long for this world." And... you're not heartless: you care. And when asked "Can he spend a week at your place, so that he can be close to the hospital for some treatments?" you go along with that because you know it's the decent thing to do. Have you no empathy after all? Of course you'll do it! To not care in the midst of that suffering? Pah. 'Course not!
...only after the first few hours realizing he's dying, you realize also... that he's still a jackass. And you can't tell anyone he's a jackass, because that's insensitive - he's dying! You can't call the dying man a jackass just because he does something only a jackass would do! But yet, it's everything you despised about him running on a loop 24/7, until by day five, you see him on the couch... using the blanket your dead mother knitted for you as a napkin, watching pay-per-view wrestling, and spilling your last beer all over that autographed Terry Pratchett novel of yours, and you finally say to him, "Good news! You're not gonna believe this: you're not dying of a terminal disease... because I'm going to fucking kill you FIRST!"