[Robert Morris] “anyone else annoyed at AE’s bug where the tangency of the bezier handles break apart for absolutely no reason.”
Nomenclature:
Smooth point: both handles move simultaneously, opposite each other, creating a smooth curve.
Corner point: both handles move independently, creating a sharp point.
Regarding the smooth or corner nature of a point, the ctrl/cmd button is used to invoke the convert vertex tool (the chevron) to change the handles from whatever state they were in to the other state. So once you change them from smooth to corner (or vice versa), if you want them to stay that way, don’t use the ctrl/cmd key when you drag.
You can’t move both handles of a corner point simultaneously, by the way.
Steve