The desire for more years is not wrong in itself; a longer life can be used for worship, learning, and service. The warning is against endless craving that prevents a person from using the time already available.
Example: One student keeps postponing study and good deeds while waiting for a perfect opportunity. Another makes a manageable, consistent effort today. The second is making better use of time.
ابْنُ آدَمَ is an iḍāfah construction: ابْنُ is the first noun and آدَمَ the second. It refers broadly to humankind in this context.