I’ve seen what you describe and, as the others have suggested, it is due to incorrect use of layers. This is a good example of why we advise you to always leave ungrouped/non-component geometry associated with Layer0.
If you select a cylinder that is not a group or component and assign a new hidden layer to it, the softened/smoothed edges of the cylinder remain associated with the original layer and consequently SketchUp displays profiles for the (no longer visible) surface associated with those edges! Profiles are a sort of “virtual” edge that you can’t select or edit, so the situation is very confusing!
You can prove this to yourself in either of two ways: turn on view->hidden geometry and you will see the softened/smoothed edges as well as the profiles, or edit your style to turn off profiles and the mystery profile lines will disappear.
You can avoid this if you triple-click to select everything or if you turn on view->hidden geometry before you do the selection.
Some time ago I posted a discussion of this behavior, calling it an “inconsistency bug” because if you select the cylinder the same way and use the move tool on it, all of the edges and faces move together. So why don’t all of them also get associated with the new layer together? Trimble recognized the situation but hasn’t done anything about it, probably because they feel it is a user error rather than a bug.