We literally cannot be the last species aside from bacteria to go extinct because we eat other species. We rely on plants and often animals to provide our nutrition. We rely on pollinators for plants to grow fruits and vegetables. We were able to survive those harsh environments because they could provide for us. There is no living in the artic without the seals for example.

This is also the fastest our climate has ever changed. Yes the climate has changed in the past but never ar the rate it is now which could cause widespread species collapse, likely becoming earth's largest extinction event to date. We have no idea the extents that current climate changes impacts will have on us in 100 years, let alone the fact its still getting worse as there is a significant lag time in terms of the effects.