No point to it.
Logic bounces off these people like ping pong balls off of El Capitan. As I pointed out in another post, many of them seem to be incapable of actually thinking rationally, although they are very good at memorization.
There are examples right here on this board.
The inconsistencies I point out have been pointed out by many others already, and while they give us some amusement at the expense of the anti-war crowd, the effect on that crowd is negligible.