Copy and Paste in X11 works very differently than in Mac OS. To run X11 on a Mac, Apple had to integrate the two different paradigms.
In X11 there is no copy -- any text selection is immediately on the clipboard (but you can only have one selection at a time, across all X11 windows). Paste is done using the middle mouse button. In Apple's X11, a preference setting allows a keyboard shortcut to emulate the middle button. Thus, to copy and paste, make a selection, then paste with the middle button. There is no copy step. This works within X11, but not between X11 and non-X11 apps.
Outside of X11, copy using the usual Mac procedure. If there is no selection in X11, the Mac clipboard will be available as the X11 clipboard, but you paste into X11 using the X11 method. As soon as you make a selection in X11, it overrides the Mac clipboard (but only within X11). To copy from X11 to non-X11, use Edit>Copy to copy the current X11-selection into the Mac clipboard, then Mac Paste is available outside of X11.
I am sure you are thoroughly confused now. I don't know how it could be integrated any better without breaking either the Mac interface or the X11 interface or both. You'll have to play with it until you get the hang of it.