Biodiversity [life in all its variety] should be valued for reasons of: ethics; aesthetics; ecology; education; recreation; economics; and the resilience that comes from diversity in systems. I suppose preserving biodiversity basically comes down to the fact that it exists, the fact that we like it - and the fact that we need it.
Lets focus in on how and why we need it - and in fact cant live without it! Basic life support systems - those that process our water, soil and air - require varied forms of life, so this alone makes biodiversity essential.
What follows is a list of just some of the uses humans make of biodiversity directly - it shows that it is the source of our resources and the basis of our lives: wheat, rice, potatoes, vegetables, meats and the other stuff we eat; construction materials like wood and bamboo from plants; cotton, paper, linen, and wool from fibre producing plants and animals; renewable fuels, like coppiced willow; latex from rubber trees to make tyres and condoms; ornamental plants for our gardens; tropical fish as pets; large natural/seminatural areas for eco-tourism; many species used as biological pest control for our crops eg ladybirds; reeds beds that clean up sewage-contaminated water; many pharmaceuticals, now synthesised, but originating in natural products eg aspirin from willows and penicillin from fungi...[many of these are pictured, click to enlarge].