Well, first thing is, “heading for the door” is inevitable for us as individuals, why wouldn’t it be inevitable for us as a species? Does it make sense to mourn the inevitable? I guess since we often grieve the death of individuals, we might also do so for the species.
But it’s not obvious to me that it makes sense to identify as a member of the human race, rather than as an element of Gaia. After all, humans cannot survive in isolation. We depend on plants and animals to feed us, bacteria in our gut to digest our food, entire ecosystems to produce our oxygen and process our waste. Does it really make sense to draw a circle around homo sapiens and say that is “us”, excluding all the other living things essential to our survival, inherent in our existence? Would it make sense to draw a circle around your brain, identifying that as “you” ignoring all the ancillary systems (heart, lungs, gut, etc. etc.) essential to the survival of your brain?
Since the human race doesn’t seem particularly essential to the survival of Gaia, does it make sense to mourn its passing? (The human race appears to be nowhere near as central to Gaia as your brain is to “you”.) Would you mourn if your hair fell out? (Well, maybe a little. Especially if I was a hair.)