I left mouse on work computers, althoigh I'm right handed, and right mouse on personal computers. (ergo at my first real job encouraged left mousing, and I found mixed mousing is best for my wrists)...
Anyway, most computers you find in the wild are setup for right mousing. Most mice are sculpted to be used by a right hand, a minority of mice are ambidextrous and can be used by either hand well (although it's not unusual for an ambidextrous mouse to have buttons for a right thumb and not for a left thumb), and I can't say I've ever seen one sculpted for a left hand. Same deal for trackballs; if you want a thumb trackball, it's got to be operated by your right thumb.