When using the Pick Address From Map tool, the left-click button is used to view addresses at the mouse location. Right-click > Pick Address actually picks the address.
However, for faster rematching, mouse clicks can be saved by using the short cut keys. This saves from having to left-click a point (for the Match To Address Location option) and then right-click > Pick Address.
The left-click is optional for the Match To Click Point option, but is required for the Match To Address Location option.
To place an address without using the context menu, hold down the left mouse button and press the spacebar.
See the link to the Rematching a Geocoded Feature Class in the related information section below for more detailed steps.