People often suggest one role of a leader is to convince people to do something.
I disagree.
People seem to associate the act of convincing with the outcome they want. If convincing worked as people wanted, I would associate them too, but I see it work differently in practice.
If someone disagrees with you, using logic to convince someone still depends on your premises. So if the person doesn’t agree with you, you have different premises. They’ll see your attempts at convincing as imposing your values on them and push back, leading you to convince more, and so on. Argument ensues.
When people agree there’s no point in convincing either since you already agree. Trying to use logic sometimes provokes argument even when someone agrees.
If you think of convincing as a way of influencing and persuasion, you’re making yourself ineffective.
You are leading them, just rarely where you meant to. You’re leading them to argue with you. If you get annoyed at them for arguing with you, you missed your role in provoking the debate.

My model for convincing: It’s a synonym for “provoking an argument”

I’ve adopted a model for the act of convincing as a synonym for “provoking an argument.” Sometimes the model oversimplifies, but rarely. So when I catch myself thinking I’ll convince someone of something, I think to myself, “do I want to argue with this person and risk alienating them?”, because that’s the usual outcome.
Then I work on my other skills of influence, persuasion, and leadership.