I read "Darwin's Black Box" over 20 years ago so I can't give a lot of details. His fundamental idea was "irreducible complexity", a system that won't work if you take away any piece, such as a mousetrap. He claimed that a lot of biological mechanisms were like this. The fundamental argument was that something irreducibly complex can't be formed by evolution because it won't work if is anything missing, so you can't evolve part way. E.g. a mousetrap that lacks the spring doesn't work at all. Therefore, evolution couldn't create the irreducibly complex mechanisms found in biology. QED.
The big flaw that I see is that he looks at the problem of creating irreducibly complex mechanisms by addition, but they can easily be produced by subtraction. As an analogy, an arch is irreducibly complex because if you take out any stone, it collapses, so you can't build it one stone at a time. But you don't build an arch this way. Instead, a support is built and the stones are put on top of the support, one at a time. When you take the support away, now you have an irreducibly complex structure. Similarly with biology, something can evolve step by step with redundancy, and then pieces are removed by evolution, ending up with an irreducibly complex mechanism that Behe views as impossible.
I should reiterate that I read the book decades ago so I'm probably wrong on the details of Behe's argument. I figured I should answer your question but I'm not particularly interested in having a debate on evolution.
The big flaw that I see is that he looks at the problem of creating irreducibly complex mechanisms by addition, but they can easily be produced by subtraction. As an analogy, an arch is irreducibly complex because if you take out any stone, it collapses, so you can't build it one stone at a time. But you don't build an arch this way. Instead, a support is built and the stones are put on top of the support, one at a time. When you take the support away, now you have an irreducibly complex structure. Similarly with biology, something can evolve step by step with redundancy, and then pieces are removed by evolution, ending up with an irreducibly complex mechanism that Behe views as impossible.
I should reiterate that I read the book decades ago so I'm probably wrong on the details of Behe's argument. I figured I should answer your question but I'm not particularly interested in having a debate on evolution.