Here's a plot device that an entire genre of movies is devoted to - indeed, the "buddy cop" movie - wherein two police officers are partnered together who are polar opposites in terms of temperament, ethics, and often race as well. They usually begin with a strong dislike for one another - though, as in the genre's best example, Lethal Weapon, this isn't a requirement - and over the course of their partnering together, they come to an understanding that makes them a savagely efficient crime-fighting unit. The fact that it's a genre unto itself says a lot about its popularity, and audiences apparently don't seem too fazed about how predictable and generic these films can be in the wrong hands (i.e. without Shane Black). Nevertheless, have you ever watched one of these films and been surprised? Given how much character plays into films of this sort, the success of a film like this usually hinges on casting.