Apparently Cavill's agent has responded to the rumors of him leaving, the exact quote: "Be peaceful, the cape is still in his closet. @wbpictures has been and continues to be our partners as they evolve the DC Universe. Anticipate a WB statement later today." And WB's official statement was: "While no decisions have been made regarding any upcoming Superman films, we’ve always had great respect for and a great relationship with Henry Cavill, and that remains unchanged."  Which, ehh, is kind of a non-answer, so take that as you will.

Sounds to me like folks heard that his contract negotiations weren't going as well as they wanted and started jumping to conclusions, like how Ben Affleck hasn't been able to sneeze for the past two years without everyone going "OMG THIS MEANS HE'S QUITTING!"  Given how WB has been a completely disorganized clusterfuck, and given how much shit-flinging sites like Hollywood Reporter and Screen Rant do to bring in clicks, who knows how much of any of it is actually true.