Thank you for your question. To be efficient in answering, I will need time to "collect my thoughts" and try to express them as succinctly as possible.
On a related note: I have repeatedly heard the assertion from "historians" that Jews had a view of the nature of the human person that was far more "integrated" than the "Greek" view. This is not a Biblical claim per se, it is a claim that those who have studied Jewish culture have come to the conclusion that Jews did not generally believe in the model of a physical body which "housed" a non-physical soul that was the seat of consciousness. Instead, the Jews generally believed that you could not "split up" the human person into "parts". Again, this is an historical claim, and you have asked for a Biblical argument. While the two cannot be strictly separated, I will try my best to anwser your question as soon as possible.
The major pitfall of the dualistic model is that it implicitly endorses the view that the "physical" is of a lesser order, or importance, than the "non-physical". This leads to (incorrect, in my view) thinking like (1) we will spend eternity in heaven without bodies; (2) God is going to burn up the present physical creation.
Such errors lead to very real consequences - for example, lack of appropriate stewardship of the environment, based on the premise that since this world is going to be "thrown away anyway", there is no real need to be overly concerned about preserving it.
Big mistake, in my opinion.