右 is a right hand paired with a mouth: the hand most people eat with. Its older form was the ancestor of 又 'again' — the busy right hand that does everything, again and again.
尊右 'honoring the right' dominated later dynasties: 无出其右 'no one stands to his right' still means 'second to none'. Traffic in China keeps right too — 靠右行驶 is one of the first signs you'll see on the highway.
The hand 𠂇 that feeds your mouth 口 — for most people, the RIGHT one.
座右铭 'motto' literally means 'inscription to the right of your seat' — ancient scholars carved reminders where the writing hand could always see them.