The obvious thing to recommend this view is that intuitively, we "feel" that our mind is very different from anything material (absence of weight, size or extension for instance) and also that our mind is unable to fully grasp what matter is (= the Kantian idea that our mind cannot access the true essence
of things, only their appearances).
So it does intuitively feel like mind and matter can't mix, just like oil and water. That there is a gulf of differences between those two.
Another argument is the duality between wave and particle. If each and every physical particle in this world can also be described as a wave, then it is possible to think that each living entity can be described as a combination of body and soul. Cartesian dualism is not more shocking to the mind than the idea of a wave-particle duality.
However, we know empirically that mind cannot exist without body, ever, and that once a person's brain is cut in multiple pieces, nothing much seems to remain of his mind. Therefore it is logical to conclude that the body gives rise to the mind, that it produces it. And thus it is logical to conclude that mind and matter are not totally strangers to one another. Matter can create mind, and mind can affect matter (through decision making).
In the end, it is the word "substance" which is not very clear here. What is meant by "two substances"? Can, say, matter and information be perceived as "two substances"? But then, what substance composes a poem writen on a sheet of paper? Is the poem's substance the ink and paper, or is it made of signs (letters, words), or is it made of ideas and images?
Come to think of it, what is the "substance" of the body? Matter? Energy? Wave? Information?
The concept of substance is pretty vague, as I see it. Perhaps it's just another failed attempt at grasping the essence of things. Then the question does not really matter. What matters then are the relationships
between body and mind. How does the body give rise to the mind? How does the mind control the body (to an extent)? These are to me much more fascinating questions than "what substance are they made of".