While you're checking the tread depth, put the bike on the center stand, and slowly rotate the tire, and take a good look at the tread area, checking general condition for cuts and other damage.
I have only had one Metzeler front tire cup on me, it was on the left side.
It was also during the time, that I ran the bike without any oil in the left fork.
I got interrupted during a routine fork oil change, when I got a call, that a friend needed a ride the the emergency room, due to an allergic reaction, thought I had serviced the left fork, when I hadn't.
I use a check list now to prevent it from happening again !!!!