It's just not a useful argument for saying "FTL is possible" because if you accept that, then X is possible for all X, and "impossible" has become a meaningless word.
I think this is exactly the point, for both sides. I have no special interest in dignifiying the word "impossible". In fact it's a pretty devious word, which constrains our thoughts and perception. Why care if its meaning becomes less significant, that may actually be a good thing.
To the point, I think we should distinguish between "according to today's knowledge of science and physics FTL is impossible" and "FTL is impossible". The latter of the two doesn't take the fact into account that our scientific knowledge is far from complete and will continue to progress over the coming decades and centuries, which could open up new possibilities. Maybe FTL won't be one of them. But as long as the possibility exists that it could be, which we cannot yet foresee, we shouldn't be too definite with our statements.
The core of the disagreement here seems to be not so much disagreement in itself, rather the clash of physical and philosophical standpoints, which both, in their sense, are perfectly correct.