Even stars like our sun die. Does the second law of thermodynamics ultimately kill. There is a time we didn't live will there also be a time we don't live in the future. We already have not lived indefinitely.
Well, thats true.
Anyway, like a star, a rock or the mouse of your computer; the biological structures are formed by matter. All structures formed of matter suffering some kind of wear. The difference is that the biological structures have the ability to regenerate that wear. Like the skin of a snake, the matter of which we are made is constantly changing.
We do not know why aging exists (life probably would not be possible if species not die after some years of life), but from biological point of view, live without agein is posible, so unlike a star, we can regenerate our wear forever (in theory).