My guess is that you (or anyone else) doing the work he should be doing is a reminder of his inability to accomplish the task, which in turn makes him feel worse about who he is or what he is doing. It has nothing to do with you.
Do you have a friend or family member that has the tools and could help you complete your projects? He probably won't like that either, but a sandbox or play set for the kids isn't about him.
They are pretty useless when they are active. My RAH wants us to go to an orchard this weekend & brought up one we went to a few years ago thinking we went last year. I told him that I went by myself last year because he wanted to stay home to watch football & drink beer. It's so sad to see what they miss out on...and can't remember.