If you're just not buying it, you're unconvinced. When it comes to music, people will often try to sway you to their way of thinking — that a band is THE band — especially if you remain unconvinced.
The word unconvinced has convince as its base. The latter is from the Latin root words com, which is an intensifier, and vincere, which means "to conquer." The prefix un means "not." So unconvinced is "not conquered" or "not persuaded." If you are unconvinced that taking the new job is a good move, why not ask for more money or a corner office?