To curve the stroke by the selection tool it must not be selected or grouped..
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It sounds like you a using the line tool with Object Drawing mode turned on. To see if this is true, select the line tool and look for the sub-selection feature called Object Drawing located near the bottom of the toolbar. Key shortcut "J" will toggle this on and off. Object Drawing is available for several other drawing tools.
When you draw with Object Drawing turned on, you will notice a box around the shape or line you draw when it's selected. You can do one of 3 things from here:
1. Deselect the object and now use the Selection tool to bend the line
2. Break apart (command + B) the object on the stage and then edit as necessary
3. Double-click the object and edit from within the "container".
Hope this helps.