Builders name a figure before laying a brick. Nobody finds this arrogant. The work hasn't happened, the outcome isn't known, and the number gets stated anyway, because otherwise there's no basis on which to begin.
Claiming in advance isn't prediction. It's a decision about what you're doing, made while you still have the standing to make it, rather than negotiated afterwards from a position of exhaustion.
Most people who struggle to charge properly are trying to price the work once it's finished, which is the worst possible moment to be brave.