The fact that it relies on an absurd belief.
Rabbi's are inspired by God, God created us and inspired scripture and knows what is best.
Yeah. That's the irrational part.
But it is a rational argument, it applies known (to the subject) facts in a logical manner to determine the true course to take.
"God told us to" isn't logic unless God is first proven.
The question of whether God exists is not a scientific question
Yes it is. If God exists, there should be a proof for it. If there is no proof, then there is no God.
"Rabbi's provide bad advice" might be a good first hypothesis - eventually we see that Rabbi's usually provide good advice, should we take that advice? Seems logical (within this limited discourse).
That's a non sequitur. If a rabbi (not a proper noun, by the way) provides good advice, that proves that the rabbi as a human being is wise regarding certain things. I can give terrific personal advice and still not be good at playing the stock market.
Well do we have scientific data which somehow shows his premises to be wrong?
You're invoking Sagan's dragon. The burden of proof is on you, not on reality. Until you prove it right, you are wrong and have no argument to make.
We belive they are wrong but can't readily show they are objectively wrong.
But we can.