The following is an answer and/or comment by inhahe aka ColorStorm (inhahe.com - myriachromat.wordpress.com).
Part of it is biological. Billions of years of survival of the fittest have programmed us to avoid death at all costs. And part of it is spiritual. We're actually eternal beings, with vast histories of loves, joys, and experiences in general, and that's all in us, recapitulated in every interaction with a loved one, every emotion, etc. Because death appears to us as the dying of the light / the snuffing of the divine spark, or at best the utterly uncertain, it's terrifying because of how precious we know ourselves and our potential for future joys, on and on, to be. If I'm wrong and our lives are not eternal, I'd still say the fear of death is due to an underlying knowledge of how precious our love, joy, and potential for future shared joys are.