Why would all life perish?

All life wouldn't perish, the only things that will be left will be certain bacteria, phagocytes and viruses that can tolerate and indeed will likely proliferate in extreme environments. Everything larger then that will die of starvation due to a cascade of failing systems, likely starting with the death of the marine biosphere when the temperature rises to unsustainable levels and/or the pH lowers too much for the same effect. Though of course no one really knows what will actually happen because there are too many unknown variables.