I could be totally wrong, but I didn't believe it was Homelander that Butcher was talking to in that one scene.

At first I thought that Homelander had really come to see Butcher, and that he actually sat down at Butcher’s table to talk with him. But then when Butcher looked away for 2 seconds at the end of the scene and Homelander suddenly wasn’t there, I was thinking that the conversation was actually all in Butcher’s imagination. I think maybe Butcher was actually talking to a mirror reflection of himself, admitting to himself that what he wants “more than anything” is to go mano a mano against Homelander in a battle to the death. The fact that Butcher has access to superpowers with the Temp-V now makes it possible, he realizes, for him to fulfill this deepest desire of his.

I also think this is the case because the Homelander in that scene just did not sound like Homelander to me. Homelander would never talk about “sharing a destiny” with someone like Butcher or respectfully say that he “looked forward to” a scorched earth battle to see which one of them would be left standing. Homelander does not believe that anyone, much less a mere ordinary non-supe human, is his equal. He thinks of himself as a god who can squash any mere mortal who challenges him like a bug.  Also, the frustration that Homelander shares, his anger against "Vought and the Bureau", at all the "wheeling and dealing and giving and taking, just to keep everything exactly the same", sounds exactly like the frustration that Butcher is feeling about the past year and that he expresses to Hughie.

(Plus I don’t believe that Homelander would just silently disappear when you are turned away from him, as opposed to making a dramatic exit while you were watching.)

So this scene goes to the heart of Butcher’s motivation for using the Temp-V. He doesn’t just want the destruction of Homelander; he wants to take him down personally in a final apocalyptic battle.