I like to work in the dope sheet and if you have the object selected in the hierachy on the left, when you selects keys to delete the whole object deletes. Deselect the object on the left, then select and delete individual keys.
Not sure if something similar is going on in curve view. Wouldn't surprise me.
Is this a specific curve-editor q?
In that case, you have to select the individual XYZ (Crtl to add) positions and drag a square around them and press delete.
If it's a general q, then there are more options:
In the timeline, right-click key 15. There should be a menu pop up and in there a delete key,with sub-menus for positions, rotations etc. even for indivdual XYZ axis.
Another way is to select your motion tab. With the ball selected, there should be PRS Parameters rolled out. There you can delete or create keys for positions, rotations, Scale. (Be on frame 15 in timeline to do this). That's for all axis.
Or as said, in the dope sheet 🙂
Edit: It works like that in 2013. Currently I've not tried 15 yet, but I'm sure it's the same.