I have this rectangle with of course a border around it on all four sides. I would like to delete two of these sides so you have a rectangle with only two colored sides instead of four. The problem is that the scissor tool does not work.
Simply add an anchor point with the pen tool in the middle of the path(s) you want to delete, then select that anchor point with the white arrow (direct selection tool) and delete it!
You do what I suggested above for one side.
Then you can do what I suggested above for the other side as well.
If you want to keep some filling, you'll need to add a rectangle with no stroke and send it to the back... with your 2 strokes left on the foreground :D
If you need to delete 2 paths that touch each others, simply use the white arrow (direct selection tool) and select the corner of these 2 paths... then press "delete"
You should think about the
Stroke as a separate entity. Draw your rectangle with just a
Fill and no
Stroke then use either Pen or Rectangle to create the
Stroke on the sides.
Alternatively if you already drew your Rectangle (or any shape really) with a
Stroke then you can use Expand to separate the Stroke from the Fill and then manipulate it how you'd like to.
Groups (Ctrl/Cmd+G) to keep the parts together.