Because as he keeps saying over and over -- the only "peace" he will accept is one in which his claims to sovereignty on the territories he is currently sitting are recognized by Western powers. This was his core demand during the Istanbul talks, and it's his current demand now (though he's upped it a bit recently to include regime change in Kyiv).
For a serial territorial aggressor like the modern Russian state, "peace" is simply another mechanism for arriving that same the desired end state.
It's also useful as a propaganda tool, to mollify the opposition to what he's doing ("See, Putin just wants peace -- he even says so!"), get people to start talking about how costly the war is, how the West is the real aggresor and so forth. That's where Mearsheimer et al come in.
