Okay Cking, I have a final challenge for you. Tell me whether B and C form a paraphyletic or polyphyletic group in this example:

The relationships among the taxa are ((A,B)C)(D,E). The character matrix is:

A - 000
B - 111
C - 111
D - 000
E - 000

Lets assume that 1000 other characters support the above relationships perfectly (i.e. no homoplasy), so the relationships are not ambiguous. Using a character based definition of para and polyphyly (which you appear to prefer), I argue that there is no way to distinguish between between para or polyphyly, but it is clear that these two species do not form a monophyletic (i.e. ancestor and all descendents) group. This is what I suggested could happen, while you denied it is possible. In this case it is clearly correct to state that B and C are not monophyetic (unless you and I disagree on the definition of monophyly), but it is not clear whether they are para or polyphyletic. Hence the appropriate use of the term non-monophyltic. If you can prove that there is a way to tell whether B and C are para or polyphyletic, I am very interested to see this proof.

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