An alternative to the Motive Rant has the perp, when cornered, explain how the murder was all an accident. Their excuse can be almost anything, but the most common explanations are
"It was just a joke!", when a prank or practical joke goes horribly wrong.
They were having an argument with the victim and accidentally shoved/nudged/chased them over the precipice or down the stairs.
"I didn't [...] [tvtropes.org]