But that isn't the claim. The claim is that mind appears to be generated by matter (materialism). What we see is most consistent with that. Yes, there are other logical possibilities (idealism, neutral monism, and dualism), but the evidence for them is scant, and the materialism model works well to explain the observed relationship between brain and mind. Changes in brain lead to predictable and reproducible changes in mind.
The fallacy is to insist that this cannot be the case because a mechanism is as yet unelucidated - an ignoratiam fallacy.
Let's consider the alternative hypotheses. There is nothing to support Cartesian dualism to my knowledge. Neutral monism has always appealed to me simply because physics has been a series of unifications since Maxwell unified electricity, magnetism and light. These were wed to the weak force (electroweak) and then the strong force (grand unified theory). Space and time have been wed. Position and velocity uncertainty have been connected. Energy and matter as well. Will mind and matter be next? Will we be able to discover some kind of conservation law where more of one means less of the other the way that in a closed system, more ice means less water and vice versa (ignore evaporation and condensation for the sake of simplicity)? If we didn't already know that water and ice were the result of a single substance, that relationship would let us know that they are.
So how about neutral monism? Are you aware of any changes in mind changing brain? I suspect that that can happen, that persistent habits of thought might lead to perceptible change in brain architecture over sufficient time. Also, experience leads to new neural connections. How do we incorporate these observations into our model for the relationship between mind and brain? This and the series of unifications I just named are weak evidence for that possibility.
Idealism is the last logical possibility in this list. The theist has already decided that reality is an idea of God, that God is thought, and that this mind is the original substance responsible for and underlying material reality, so he can be expected to reject other logical possibilities out of hand.