One of the reasons why that particular exchange (and the entire short Rabbit Fire) is so enduringly culturally resonant and funny to this day is because we are all Daffy. The book Chuck Amuck discusses this.

Prior to that cartoon, Daffy used to be screwball Totally bonkers. Hence the name. He used to exhaust and beat down those he came up against. Not so in this cartoon. In this cartoon, he's more. He's the viewer.

As a character Elmer Fudd is an idiot, we can all agree. The straight man with a funny voice. He never knows what's going on and can always be bested. Bugs, on the other hand, lives at the place where wiliness and comedy brushes up against the insane.

In this cartoon, Daffy is a straight man but immensely more relatable than Fudd. He is smart enough to understand the absurdity of things like tearing the hunting season poster repeatedly off the tree, but he's not quite wily enough to escape the game. That is, until Bugs himself rips the poster down revealing it to be Elmer Season.

You can read the scene as Daffy being graciously let off the hook by Bugs. He's slightly less than one step behind Bugs. If you watch the scene, particularly at a slower speed, he even emotes much more slowly than Bugs. Animators don't waste frames. It had to be intentional on their part, a subtle cue. Daffy's been bested, but was clever enough to have a truce called to his benefit.

We laugh and laugh years down the line, because we're all just as reasonable as Daffy but still want to be part of the fun. I think the cartoon's a masterpiece.