The reason is more physically related. Most of the horses' strong side in left, like most humans being right-handed. Therefore, it's better to approach a horse on his strong side so he won't feel intermediated. Also, it's better to climb a horse on his strong side so he won't lose his balance while you climb.
Nowadays it obvious that most horses, being domestic, can manage if approached from the right side. But due to historical reasons all of the equipment is based on the horses' strong left side.
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