I don't know about you, but it seems someone at WB wanted to see Bugs Bunny with someone else for a change, as opposed to Elmer Fudd or Yosemite Sam or Daffy Duck, as a foil. Chuck Jones decided that Wile E. Coyote, erstwhile nemesis of the Road Runner, would fill the bill.
Wile & Bugs teamed a few times, including one memorable occasion where Bugs actually was a stand-in for his "fast-feathered friend", as he'd intro Road Runner on their CBS Saturday morning show years later. However, we're taking you back to 1956 and "To Hare Is Human", which posits a talking Wile as a genius, right down to having a business card. He is so brazen, as you'll see in the first moment of the picture, to break into Bugs' domicile and capture him. Of course, you realize this means war!
It's just too bad they couldn't do anything to reciprocate for the Road Runner, but then, sending Elmer after him would be a lost cause.