Now you are asking questions I haven’t read any answers to. Go to YouTube and watch a super slow mo of archers paradox. Arrow flexes or bends toward the bow/away from bow hand first because the heavy tip is to the left of the nock, and when the string is dropped, it travels toward the bow in a plane that is to the right of the point. The tips inertia is what it is...and the energy from the bow thru the string is trying to send the nock end of the arrow straight through the center of the handle.for RH shooters...because the nock is to the right of the tip...the first flex will be arrow Boeing to right. Imagine hammering a long finishing nail into concrete and placing the tip of the nail just a hair left of the head of the nail and giving it a whack, the nail will bend curving to the right.
As to why it does not flex up and down...especially since most nocking points are noticeably high...not sure on that one. It probably has something g to do with lateral forces overcoming vertical forces that involves math no one can comprehend...since it does not happen to a noticeable degree, its one of those things I choose to just accept and not think about...too much other clutter in my brain already.