Classic meltdown, killed her in a fit of rage. They probably fought, she probably made fun of him being only half a man, and this was all it took. He attempted to reclaim his masculinity in a fit of rage and gunfire. GUILTY!
Oscar reminds me of the typical American Gun Nutter, obsessed with guns and eternally afraid and fearful, this is the only other explanation, his paranoid fear spiralled out of control and it overtook his common sense and reason. And what do gun nutters do when they feel fear? They grab their guns and start shooting.