In my view its a simple category error, though of a subtle kind. Machines are similar to biological systems in only the most superficial ways: they are non-static systems which exceed a certain complexity and they both follow the laws of physics (see footnote).
There are a lot of ways to think about the differences between machines and people. One very simple one is that machines typically function in only a very limited subset of the space of their available degrees of freedom and small deviations are usually catastrophic. Biological systems don't usually have this property.
Another way to think about it is that machines show evidence of design, which you might characterize as a certain economy of ideas. Two clocks in a computer a much more likely to be identical or to share major conceptual underpinnings than two clocks in a biological system, for example.
I used to have your view of things and then I read Deacon's "Incomplete Nature," a book whose thesis fails to land but is never the less a comprehensive analysis of the properties of living organisms in a unified if rickety system which encompasses the basic laws of physics. It really convinced me that the analogy between brain and machine is poor.
The question of what a mind is and how it relates to the brain is not settled science or philosophy, at any rate. It doesn't do anyone any good to pretend it is.
(footnote): This is a reasonable assumption to make but its hardly widely believed by the general public nor settled scientific fact. Luminaries like Penrose still assert a fundamental disjunction between what brains do and what machines do and he isn't alone among physicists, to say nothing of the broader philosophical community or the lumpen mass of human opinion.