As reported here — https://www.reddit.com/r/AdobeIllustrator/comments/1p6pyau/what_do_i_not_understand_about_snap_to_point/ — modern Illustrator is having problems when dragging live shapes by the center, expecting this center to snap as a point to another points.

Live shapes like start, ellipses, rectangles, now have the additional widget controls displayed over the bounding box — to alter the shape on canvas. Well, this fat dot in the middle seems to obstruct the REAL center point shapes get when created.

That’s why disabling the bounding box helps — the fat dot vanishes with it, exposing the real center point (Attributes panel control it being on or off).
That’s why using the Direct Selection tool helps — the bounding box appears only when a shape tool or Selection tool are used.
That’s why expanding the shape helps (either with Object > Shape > Expand Shape, or something like Pathfinder > Add — but it’d require for center to be reenabled) — the live shape widget shows up only for live shapes.

This widget wasn’t a thing in older versions, and there was a time it worked fine after live shapes were introduced, until the fat dot happened. Please make it work. Today, even with enabled Smart Guides Ai might (within a tolerance) display the 'center' when you hover over the fat dot obstructing the center, but would not register it as one when you start dragging. Shame!