My wife is in hospice at home and is not eating much, why do I feel guilty when I eat?

This is such a sad time for you, it’s not surprising for your emotions to be all over the place. Eat as you feel you can, you’ll need strength for the days ahead, your wife is depending on you in her final times. I wish you both peace

Your wife would not want you feeling guilty for eating just because she no longer has much of an appetite. I'm sure she wants you to take good care of yourself and that includes you getting the proper nutrition.
It's very normal when one is nearing death to not want to eat or drink much, so if it makes you feel a little better perhaps try eating in a room away from her.
I wish you well as you take this final journey with your wife.

It seems like your mind is grieving. Be assured that your wife's decreasing appetite does not mean that she is hungry. Just periodically make an offer