A center of mass is acted upon by external force (inertial acceleration) or pursues a minimal action geodesic path through space (gravitational acceleration). Why is any of this a mystery?

A center of mass is zero dimensional. That is smaller than atomic.

Linear acceleration is rather boring. Angular acceleration is much sexier. You don't see vigorous tap dancing like Mach's Principle or frame dragging decorating linear acceleration.

Physics is about "how." Religion is about "why." If you want a working flush toilet, empirical observation suggests "how" is a much shorter and more fruitful path than "why." Vatican toilets are the products of engineers not priests. Test of faith!

Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf