Lots of reasons.
I was always fascinated with the idea of where I came from ~ as in right back in time! I know that I'm not likely to find that out, but my interest in the origins of man & the 'Out of Africa' theories, etc, fascinate me as much as finding out about my great grandparents. DNA 'archaeology' is making this side of my quest a real possibility now. (Expensive idea though

)
Before I started on my own geneaology I would study the pedigrees of the royal families of Europe. Again, I was fascinated.
I love history, archaeology, anthropology, etc. When I was studying History at school it would come alive for me when I realised that members of my own family had lived through it ~ especially if they were people I had known.
One day, my Mum heard a geneaologist being interviewed on the Jimmy Young show. She thought that this was something I would like, so she bought me her book ~ 'How to Trace Your Ancestors' by Meda Mander.
I was hooked. I have ancestors from England, Wales, Scotland & Greece ~ and probably elsewhere, too. I have an illegitimate line which prevented me from researching in that area for some time, because it upset my grandparents so much when I first mentioned it.
Some of the family stories are amazing ~ the true ones more so than the 'legends'!
Without those who gave birth to me, and to my ancestors, I wouldn't even be here. I want to know where my roots lie.