Why Both Of You Push Back Against The Same Change
Resistance from a parent is usually about identity, and resistance from you is usually about permission.
When a parent says they are fine and do not need anyone fussing, it is easy to hear stubbornness. It is more accurate to hear a defence of something enormous. This is a person who has run a household, made decisions, absorbed other people's problems and been the one others leaned on. Accepting help is not a logistical adjustment for them, it is a change to who they understand themselves to be. Seen that way, a flat refusal about something small is often not about that thing at all, and arguing the small thing on its merits will not shift it.
Your own resistance is quieter and less discussed. Many adult children hesitate for a long time before stepping in, not out of reluctance to help but out of a sense that they have not been given permission. There is a line in most families between offering and taking over, and nobody marks where it is. So you hover. You ask instead of acting, you soften every suggestion into a question, and then you feel frustrated when nothing changes. That hesitation is decent and worth keeping, but it is useful to know it is operating on you.
The way through is usually to make changes small, specific and reversible, and to leave the decision where it belongs. Offering to come along to something is different from taking it over. Suggesting a trial for a month is different from announcing a new arrangement. Where a change is genuinely important, it lands better as one clear plainly stated request than as a campaign of hints. And when it is refused, refusing is allowed. An adult who is making their own decisions is entitled to make ones you would not.