Why can't I merge two points?
I drew a circle, added a diameter to it, joined objects, removed topmost anchor point...
Now I need to make it united shape:
The question is general and the situation is general: suppose I have exact parts of desired outline shape. I can't use any averaging or pen tool, because all anchor points are already in place. All I need is just declare some overlapped points pairs as single points.
Why can't I do that?
If I press Object -> Path -> Join I get a message
The command you are looking for is JOIN
Use the Direct Selection Tool
select BOTH points you want to join (I usually click and drag across the region containing them).
Click Join in the toolbar (or Cmd/Ctrl+J)
Alternately you can also select the Pen tool, click an endpoint to activate drawing with the pen (and continuing the line segment) and then touch the pen tool to the other endpoint of the half circle (the cursor will also have a small circle, to indicate closing the shape).
If the two paths are already joined (and you get the two open endpoints error), use the Unite command in the Pathfinder window.