We now casually use the Ctrl-C to Copy.
We also use Ctrl-X to Cut. I understand this choice. We cannot reuse Ctrl-C and the 'X' represents a cross. Crossing something out on a sheet of paper was similar to cutting it out.
Now... Why would we use Ctrl-V for Paste? The only thing I could come with is that it's close the other two keys and thus let's keep that functionality together...
I know that those controls have different meanings in a console. I'm not interested by the console use of those keys unless it is somehow related (I doubt it).