This question already has an answer here:
East-west directions can be misleading. Point B, which appears due East from A, will be closer to the equator than A. Thus the curvature found this way is smaller than the curvature of a circle of constant latitude, except at the equator. West can exchanged for east in this discussion.
appears on the Wiki page regarding Earth radius. This does not correspond to my understanding of the geometry for an ellipsoidal Earth: if I move due east, I'll stay at the same latitude, and thus I'll still be the same distance way from the equator.
I what sense is a point B that is due east from A "closer to the equator"?
In fact, how can this make sense? nothing in the problem setup differentiates point A from point B, so neither can be closer to the equator than the other since the problem is symmetric.
In response to duplicate question comments: whether I move from A to B via a great circle or via a rhumb line, it shouldn't affect whether one of the two points is closer to the equator than the other.