Vampires don't die from old age.
Vampires aren't born, all vampires were humans at some point in their life.
After being bitten a human can turn into a vampire (although chance is very low, otherwise vampires would run out of food). Vampires are NOT mindless monsters, they have their own personality, memory and feelings too. Also it's clear that minds of new vampires aren't "tabula rasa", they seem to have, at the least some memory and personality of their old selves. But it's also clear that something probably changed in their personality because vampires in general display attitudes like this (depends on individual vampire, so can vary):

1. "Humans are cattle, vampires are the master race."

2. "It's natural for vampires to attack humans, so there is nothing bad about it."

3. "Humans will die someday anyway, so why bother about their lives?"

4. Something something radical egoism

And it's all despite them being humans once and still having memory of human life.