Immortality sounds nice and all, but that's only in curtain circumstances and only for a limited time period. We've heard of all types of immortalities including those caused by super healing and some are just plain invincible. In the end I am of the opinion that immortality isn't something we as humans could handle.
Imagine the pain of being afraid of starting friendships as they will always end in pain. Imagine accidentally taking a slightly longer nap and notice all your friends died in that time period. Not to mention how you'll always be scared that someone might notice how you're still young even after decades and thus the need to constantly change identities. If you don't have an invincible kind of immortality, you'll become paranoid over the years that the government or some other organization is out to get you. But that is under the prerequisite that you don't eventually succumb to the pain of time and take the easy way out. But that only works if you aren't invincible.
Better yet imagine witnessing the sun die along with all the life in our solar system but still continuing to exist, floating aimlessly through space for millions of years.
It's no wonder that most immortal beings depicted in movies and anime don't give a damm about life since they've probably grown bored of it at some point. Why should you expect them to be sympathetic with someone who could never understand the pain of living. From the immortal's point of view your life is worthless as regardless of if he kills you or not, you will die eventually.