Once upon a time, there was a shul Kiddush.  And at this shul Kiddush were both Orthodox
Jews and non-Orthodox Jews.  Included on
the Kiddush buffet were gefilte fish, cholent, salads, crackers and dips.  Yes, it was a very wonderful Kiddush.
Some of the Jews at the Kiddush had learned of the custom not to eat fish and meat together
Others had not.  The wise Rabbi
had not taught it, since it was a custom, and many people at the shul were
driving to shul on Shabbos and eating cheeseburgers and other more obvious
non-Orthodox habits of the sort. 
Therefore, he was very selective about which points of Jewish law he
chose to share, so as not to overburden or embarrass his constituents.
One of these Jews, unschooled in the meaning of kosher
altogether, took his fishy plate and proceeded to load up on delicious,
steaming cholent.  Another Jew, aware of
the issue, but not quite as sensitive as the Rabbi, and with truly sincere and
good intentions, maybe, honed in on said Jew and proceeded to inform him that
he must use a new plate for the cholent, as the original plate was fishy and
therefore violated the fish/meat combo custom.
The wise Rabbi, observing the debacle from afar, shook his
head in dismay.
And thus was the term “fishplating” born.