re: 9 year old son. Right handed, left eye dominant.

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How would you go about this? He’s kinda small built and wants to get first “real rifle”. Do I let him shoot crossed over? Or start now shooting lefty?

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I’m left eye dominant but right handed. I was taught to shoot by my older cousin who is left handed so he taught me left handed. I only shoot guns and pistols left handed but wish I would have learned how to shoot a bow left handed due to the eye issue. My muscles and muscles memory makes it to much of a hassle to change.
My auto loader shotgun is lh but all my other guns are right hand. It’s not really a big deal and speed of working a bolt has never been a real issue. Some prone shooters actually shoot wrong handed actions so that the bolt can be worked with the off hand and not change trigger hand.
If you keep him on right handed guns he will have more options later in life of buying selling and upgrading if he chooses.