The other two posters are absolutely correct.
But you have two choices to do what you want as far as I know since your path is not an effect as mine was.
You can use the scissor tool to cut the segment you want to be able to select. I assume you want to move it or rotate it or perhaps resize it or a combination of those.
If you need the original path to remain intact you can take the lasso tool and select that segment of the path and do a copy and then a paste in front and you will have a copy of that segment sitting on top of the original segment which will still be part of the original path.
If you intend to alter the segment and then rejoin it to the original path then use the scissor tool approach.
