One possible answer is that the solar system is actually less than a few tens of thousands of years old, and so there hasn't been enough time for all the short period comets to disappear.
However, that proposal has to be rejected based on evidence in geology, biology, and astrophysics. The solar system is several billion years old. That is just the way it is. The mysterious phenomenon of short period comets do not make all the other evidence in geology, biology, and astrophysics go away. The evidence is quite conclusive; the earth, the solar system, and the universe are more than four billion years old;
this thing about comets do not outweigh all the other evidence.
I know you probably don't like that, but that is the way it is.
This is not a good debate tactic I think. It's the same as a young earth creationist saying that some particular evidence doesn't conclude one way or the other because the bible is so convincing otherwise. It doesn't further the debating at all.
Although, I have just one question for Confidence. What is behind this large "wall" of ice?