The veil of anonymity gives people the freedom to say the things that lurk in the depths of their minds. To do the things they only dared dream of doing before. It is for this reason that heroes and villains alike go to great lengths to hide who they are. Because with a mask, they are free of the consequence and burden of their actions. They are free of the expectations their face carries. What they say, do, think, and feel are merely aspects of this mask.
But it is not the mask that turns them into this - rather, the mask simply allows them to be themselves. The mask removes all false expectations, all warped perceptions and demented realities, and lays bare the truth of their soul.
This is why a thief wears a mask. While a mask helps obscure them from law, the mask also allows them to do that which they crave. To pluck the trinkets their fingers itch to hold, to slip away with the treasures they yearn to for. The mask allows them to test the skills they have spent hours perfecting, to practice the craft they have spent years honing.
A thief is only ever truly free behind their mask.