What is more odd is that he told people that he took the gun out, (1) when he had a perfectly good alibi in that because he expressed no interest in guns it couldn't have been him. (2) Then he wouldn't invent a story of his father had phoned him because he didn't need to. So doesn't it seem odd to you that he had the choice of two alibis that he failed to use?
But of course the real oddity is that (3) whilst they testified that he expressed no interest in guns that didn't stop them from suspecting him right from the beginning. But of course RWB did say that he destested him.
He invented the story he did to cast extra suspicion on Sheila and to try to have an alibi.
How would the fact he didn't like to shoot rabbits help him? In the meantime their testimony was all of a sudden he became interested in guns asking about getting a semi-auto shotgun and having Anthony allow him to use his gun to shoot targets.
Had the body been found the next day his alibi would be he was asleep alone- not much of an alibi.
The calll story cast suspicion on Sheila and estbalished him at home to receive the call.
The lie about tkaing the gun out to shoot rabbits and leaving it and th ebullets out was to establish there was a wepaon of opportunity available because Sheila would not have gone to seek it out herself and if she had then the gun would have had the moderator and scope attached.