But your family, your friends and relatives, memories people have of you, what you achieved, the way you affected the world around you, your output and the things you left behind, that's your spirit. In the same way you could say your spirit is in the things influenced by your existence, whether you're alive or dead.
So you never really die, and if you say there's "nothing" after death, you've been looking at your own existence from a wrong perspective. The existence of any person is not defined by them alone. You are a part of other people, and other people are a part of you.
Mankind might be immortal, but we as individues are nothing. What about all those people that has died throughout the time? Uncountable people that aren't registered in any history book, didn't have any output to give and weren't necessarily part of others, and thus weren't able to leave anything behind, from prehistorical times to the post-modern world we are in now? Those people wouldn't have a spirit going by your way of seeing it, and that mean only certain people with specific criteria can have it, which certainly sounds skewed.