Are you upset with the idea that a clone might take your place? Would you not want this to happen?
You have no reason to be upset about taking your own place if you are ok with it.
I'm not really concerned with someone taking my place, especially if they're indistinguishable form me. I do, however, have a problem with ceasing to live. I know I won't have an afterlife, so my objective is to keep myself alive, not replace myself. I see no point in replacing myself, though. I'd be ok with the method of switching biological neurons with mechanical ones on the cellular level, because those mechanical neurons may be able to function for longer, but I'd prefer to continue to use biological neurons because biological tissue already has ways to repair itself, so if we can develop a therapy to reduce entropy by some means and allow our tissue to persist longer before failing altogether, I would be happy with that.
One thing that was mentioned recently by my biology instructor is the fact that when a cell undergoes mitosis, and the threads which pulled chromosomes over to opposite poles of the dividing cell are separating from the chromosomes, they actually break off a part of the chromosome which remains attached to the thread. This implies that as you age, the very mechanism of tissue repair is detrimental to the daughter cells because each daughter cell probably lost part of it's information, which won't be repaired before those cells again divide. So, every moment after your conception entropy within your genetic material is increasing.
Even having no personal experience as a bioengineer, I still had a small idea how we might help reverse this to a degree; when we are born, we can take a tissue sample and preserve it, without permitting it to further undergo mitosis (or limit it). If we have the ability to force these tissue samples to revert to stem cells, then we can, later in your life, reintroduce the tissue to you, giving you a supplement of younger tissue that may function more effectively than the tissues that have undergone mitosis many millions of times since your birth.