The biggest problem with immortality, according to the article, is the idea of our cells being replaced by "nanobots." According to cell theory, an object isn't living unless it is made up of cells. We would have nanobots as a replacement, is that a cell? No. Therefore, we would not be living. It would make us into robots if all of our cells, tissue, and organs were made up of bots. It would just be a catastrophe.
Another reason, like multiple people have said before, is because of my belief in the afterlife. God, according to my beliefs, gave us death as a punishment. I would like to respect his judgment and die with pride. You see, if you never die, you have all the time in the world to accomplish whatever the hell you want. In turn, you'd have no pride for what you did.
At the end of my life, I want to say to myself, "Man, I lived a fucking awesome life. Would I do it again? Probably, but there are better things in store for me." I will then await Paradise. My life, I think, would be incomplete without doing what I want to do for a living. I want to teach, teach people about the world around them, allow them to come up with morals and values of their own doing. I want to have kids and allow them to explore life, that way they can know the difference between what is right and wrong.
I just want to do a lot in my life. I would not be at all satisfied knowing that I could continue this. I would like a feeling of achievement, I would not have this if I did the same thing every day forever. I can't even comprehend forever, let alone live it. Besides, the world is going to end, and I can't say I want to be a part of that. AND I would not voluntarily kill myself. I believe that is wrong in every possible way.