Here's another explanatory backstory from Jeannie Robertson, from an interview by Herschel Gower quoted in Atkinson's 'The English Traditional Ballad'. She's talking about 'My Son David':

"The thing was that David was oldest and he was heir to everything, and the other brother was a very selfish, jealous brother. He wanted for nothin', he had everything too. But he didnae want that. He wanted to be the master, you see, o' the castle or fat ever it was. And he wanted to kill his brother and become master. So his mother likit David even better than fat she likit the other one. So when he tried to kill his brother, well of course it was a natural thing for David to fight to defend his sel'. So he killed his brother."