The person is unconvinced because they don't believe that the argument or proposal is going to work. They might be unconvinced about the idea or the person who is proposing it.
She was unconvinced by his argument and refused to discuss it further.
I'm not convinced that the plan is going to work, and I want to see more evidence before we take any action.
adjective
lacking conviction
1
The opposition is utterly unconvincing.
2
The reasons are unconvincing to me.
3
The argument from history is unconvincing.
4
The precedent of passcode here is unconvincing.
5
I find the source weak and unconvincing.
6
Despite the bluster, your argument is unconvincing.
7
Excuse is unconvincing and cheapens the seriousness of the issue.
8
I like the answers to the questions, and the opposes are unconvincing.
9
The police believed that the alibi of the fifth suspect was unconvincing.
10
Unconvinced, the captain of the Titanic throws the newspaper overboard.