Dude, I also got my definition from the dictionary.
The colloquialism was misused in this instance or you made a fruedian slip...
Anyway, further explanation from the SAME SITE you got this from:
The Pot Calling The Kettle Black ( to say something about someone else which is actually true of you yourself ... )
You are the pot calling the kettle black when you point to another person and accuse that person of doing something that you are guilty of doing yourself. Example: "You are accusing me of being lazy? Ha! That's the pot calling the kettle black!"
"The pot" (for cooking) and "the kettle" (for boiling water) sit on the stove over the fire and become black from the flames. Example: "I'm tired of you always wearing my clothing!" Answer: "Aren't you the pot calling the kettle black? You're wearing my pants right now!"
The pot and the kettle are like old friends who have turned black with time; the pot only sees the blackness which is on the kettle; he doesn't see the black on himself. Example: "Here comes the guy who is always late for work." Answer: "Aren't you the pot calling the kettle black? You are usually the last person to show up!"
(The bold is mine.)
I surmise that you didn't link up to the "dictionary" you got it from because of the further explanations that were on that very site.
http://www.goenglish.com/ThePotCallingTheKettleBlack.asp
Anyway, the point of it is both the pot and the kettle are black, thus the turn of phrase speaks to how BOTH mentioned share the same property, that of blackness. If, in this case, Sessions was the "pot" calling the "kettle" black, both Sotomayor and Sessions would share the property he accuses her of.