Well, if you were certain that a good man was just murdered for trying to help you, and you were certain the murderer could only be one man, and you'd exhausted the "reasonable" ways of resolving this, I'd like to think that you or any one of us would confront, rather than sit and let it all continue silently. Burke must have a lot of guilt over, in a sense, having gotten Malloy killed. He feels a responsibility to get justice for him. If you knew, or were convinced you knew, that someone you liked and trusted had to be lying to cover for a murderer, that would make you bitter and angry.
Burke has his flaws and excesses, but if we can put aside temporarily the fact that we side with the Collinses from years of watching later storylines where they're the good guys, we should be able to identify very much with Burke's point of view. None of this is spoiled child behavior; on the contrary, he's being a man about it, acting, not shying away from conflict in a good cause. This is about murder, not about just trying to get your way.
The writers are now starting to call Burke's judgment into question though, when they reveal that he was (almost?) so drunk that he couldn't remember clearly what had happened in the crash... and that he maintains his certainty anyway. His righteous anger may rest on quicksand. I wonder if this shows a shifting of gears by the writers, regarding where this storyline will end up, and who will be guilty.