It’s not that living things die; it’s that multicellular organisms die. But why?
Every single-celled organism alive today has been in existence since life began over 3 billion years ago. This is because individual cells do not give birth, they divide. After cell division, the two cells that result are each as old as the single cell that preceded them. The cell does not become younger by dividing. (Although this may not be exactly true, see: [1])
Thus every cell in your body is over 3 billion years old.
The strategy that multicellular organisms such as humans use to project themselves into the future is to create new cell colonies from a single undifferentiated cell rather than maintaining existing colonies indefinitely. The main reason is that reproduction is more flexible and robust than maintenance, and it provides a way of starting over with a “clean slate” and slightly different genes. Complex organisms accumulate billions of errors and problems over their lifetime. Most of these errors are fixed as fast as they happen, but life takes a toll and not all problems are reversible. Just as reinstalling Microsoft Windows every so often fixes accumulated system issues, so does generating a new organism every so often from a single cell.