Disclaimer: I don't own Harry Potter, obviously.
Just a little examination.
It was déjà vu, firstly. Because Harry's blood was used to create Voldemort, he was, in an odd way, Voldemort's father (and who wanted to be a father of a monster at fourteen? Harry tried not to think about that). And just like Tom Marvolo Riddle killed his father for leaving him in an orphanage (lonely) all those years, Voldemort would try to kill his father for reducing him to spirit form (alone) all those years.
It was logical in its way, of course. Potter had all kinds of advantages with his blood and the protections involved. Taking his blood was a good way around that.
It was a bit of superstition, too. How many times had Harry Potter escaped alive from their encounters? More times than Voldemort wanted to admit. And Voldemort wanted to live forever. Perhaps some of Potter's tendency to survive against all odds would transfer to him. (Maybe Harry was injected with Felix Felicis at birth. That would be a useful occurrence.)
It was a bizarre sort of respect as well. It was like saying, "You're the only enemy important enough to have your blood in my veins."
Hope you enjoyed. :)