I'm going to chime in with an additional clarification, because I see this question from my students all the time. Even if you know this, it may help the next person reading this...the anchor points have two states: hollow (deselected) and solid (selected), just like AI. To move an individual anchor point, click outside the object to deselect it, and then select one or more anchor points.
Place the very tip of the arrow on the anchor point, and watch for the cursor to alert you that you are about to select the anchor point (with the hollow square hanging off the cursor.) The way I see this, InDesign is having a running conversation with us at all times, but without a voice, we have to learn watch the cursors to hear what it is telling us.
Direction Selection tool (white arrow) on the anchor point (hollow square under cursor):

Direction Selection tool (white arrow) not yet on the anchor point (solid square under cursor, or sometimes just a plain black arrow):

Once selected, you can move the selected anchor point and the hollow/deselected ones stay still. I've never seen this feature misbehave and I've used it and taught it for all of InDesign's life. If it does, reset preferences.

One more thought. Anchor points are tiny, and unlike in AI you can't enlarge them via Prefs. Zooming in doesn't enlarge them either. One can use accessibility commands built in to the OS to magnify, but that's the number one reason my students struggle to select anchor points in InDesign—on a HiDPI display they just can't see them very well.