Please take a look at this file and the GIF attached.
Try these steps:
1. Grab Direct Selection and select the inner arc segment only
2. Cut it
3. Delete the rest
4. Paste the segment back (I used Paste in Front)
5. Now select the point at the top. When zoomed in, you can clearly see it has an unnecessary handle — the remnant of the deleted path, not contributing into the curvature of the path in question (BTW, if you save it right now, Ai would strip away both 'appndix' handles from both ends of the path — that’s why steps 1-4 are required)
6. Pick Pen tool (make sure you have Enable Rubber Band for Pen Tool enabled in Preferences > Selection & Anchor Display) and click the top point

What should happen:
the unneeded handle should be immediately removed and the rubber band should be straight, matching the result we get when placing a new point with the tool.

What happens:
...the top point is the 'point 0' of the path, the starting point. When I click, Ai reverses the path internally, making it the last point of the path, to add a new point at the end — an expected behavior... but it seems like while flipping it, the data of the handles doesn’t get updated in the proper moment, and the rubber band grabs the reversed direction of the handle!

If I revers the path with Object > Path > Reverse Path Direction before step 6 — no problem happens.
If I click the point at the bottom instead of the one at top — no problem happens.

The issue is old, and I was able to make it happen with CC2017.
It doesn’t happen often (for me it’s like once a month), but Ai has way too many bugs and I am quite tired.
Please fix.