Biodiversity needs to be preserved. Not for some hippy dippy concern for "Mother Earth" but because a diverse biosphere means free resources for us such as air, water and food. If we destroy the environment, our cost of living will go up, quality of life will go down, and we may even kill ourselves.
Tigers are quickly becoming extinct in many parts of the world, and their loss would be a blow to the study of carnivores and mammals in general. Although humans need greater space and access to rich lands, other solutions can be found which maintain tiger populations. Otherwise, the sheer beauty of these animals would be loss for generations to come.