I understand that we all view our brains as a record of our cognisant experiences. However, there is far more at play at the molecular level than non-biologists usually consider. Brains are not magical "higher level" abstract devices. They work in concert with the existing computational machinery of the cell and the genome.
If you don't buy that argument, at least be mindful that if you don't take adequate care, you will increase your probability of getting a cancer that your immune system cannot fight. Your cells are critical. Your gut flora is critical. You are an ecosystem, not an individual. Your mind is only the deterministic imprinting that the physical world makes on you as you make your way through life.
(I'm a computational biochemist and soon to be systems biology student.)
This doesn’t mean that I think I shouldn’t take care of my body – I know that it is instrumental to me – I just wouldn’t care much if it were destroyed should I be able to continue be whatever makes me write this sentence.
Maybe this question is helpful: What do I care about? Clearly not my cells or microorganisms. I would be more than happy to dispose of my hip joint and replace it with titanium should that ever be necessary. I essentially think the same about every other part of my body.
I also don’t care about my DNA at all. If you cloned me after my death I wouldn’t suddenly spring to life, I wouldn’t be reborn as a baby, my clone would be a different person.
What do I care about, then? That, which says this sentence in my brain right now as I type it, whatever it is. It’s probably rooted in structures in my brain somewhere. Which doesn’t mean that I care about the cells in my brain, not at all. If there is a way to preserve that structure and run it I would be just fine. That’s what I care about.
That, to me, is the most important, probably the only really important part of me. The body matters but only in the sense of being a sort of tool.