The current version of GDM requires the use of the primary mouse button. The primary mouse button is typically set to be the left mouse button by default to accommodate right-handed mouse users.

Left-handed mouse users are able to configure the right mouse button as the primary button once they have logged-in. However, this setting does not apply to GDM which makes GDM non-intuitive in the case of single-user systems where the mouse is used by a left-handed user.

In my opinion, the ideal solution is to make both left and right mouse clicks have identical behavior in GDM so that both right-handed users and left-handed users experience the same interface. If I recall correctly, an earlier version of GDM did this prior to the re-write.