This is something I've noticed with older people, mainly men - the desire to do e.g. household or other maintenance-type tasks themselves, without explaining how to do it, even preferring that I'm not there. It usually happens when I ask whether I can help with these tasks, or if I ask whether they can help me with something. I'm not specifying individuals because it's something I've noticed among several older people, both within and outside the family.
For example, a few years ago when I was still a new driver I got a flat tyre and wanted to change it. I asked an older male relative if he could show me how to change it, he said "yes" but then went and did it himself without showing me or explaining anything. When I asked him if he could walk me through it he kept deflecting it so I eventually gave up. Recently I changed the oil on my car, and I just used google to find out what to do because I knew if I asked him he'd just do it himself again and not explain it.
Another example with a different relative; whenever we do DIY together he always does dangerous things by himself e.g. lifting things that are too heavy, or going up precarious ladders alone. He won't ask me for help, he'll just go off and do it. When I realize and offer to help, he refuses. If I flag up that I think it's dangerous and that he shouldn't do it, he'll either ignore me or say it's fine. Recently I heard that he injured his back by doing this.
One last example is that the smoke alarm in our house has been malfunctioning; I offered to take a look at it but a different older male relative insists on doing it himself, so he's been tinkering with it and it keeps malfunctioning, and I'm getting annoyed that he won't even let me look at it.
Women occasionally do this too, but I've definitely noticed it more with men. I'm a young, fit man so part of me wonders whether they're doing it to "prove" that they still can and that they're not old and decrepit or whatever. I don't know if they feel threatened by me being younger and fitter and out to "usurp them" or something.
What I'd like to achieve is something like the following:
Me: "Hey I need to do -thing-, could you show me how to do it?"
Me: "I noticed you're having some trouble with -thing-, can I take a look?"
Them: "Sure, give me a minute and we'll work through it together."