This long-going claim about intelligent design has been thoroughly discredited when it comes to physical structures like the bacterial flagellum. But there are a few biochemical challenge. These challenges are posed by showing a complete map of the human biochemical pathways and asking a biologist to explain how it came to be. The allotted time for the biologist is about 5 minutes. This is why I would discourage all but the most seasoned debaters to do this. That's what Ken Miller and PZ Myers are for.
I must admit I'm not a biochemist, and so this should be easier for you to read. I will also be trying to apply these principles rather broadly so there will be a few over generalizations.
Let's imagine a short part of a chemical pathway:
The chemical A interacts or becomes B and B interacts with C and then D
These steps are irreducibly complex. This is quite common for these highly specific protein to protein cascades. Maybe one or two of these chemicals are very generic and found all around the cell but you can't have a pathway with only really boring generic factors or these cascades would happen all the time and deplete resources. So maybe A is really common but this pathway doesn't kick off unless there is a specific protein interaction somewhere along the line. The more intermediate steps the faster and more specific these reactions can be.
Let's imagine first it was like this.
For this A has to be common. It could be a simple sugar or lipid glob. Insulin production for example is stimulated by the presence of sugar as is amylase.,Lipase is stimulated by lipids, etc
This pathway has two steps and so there is no change in specificity, low potential for exponential increase(because there are only two steps) and there is only one form of regulation possible(that's if the product "D" inhibits the transformation of A to D.[This is quite common because most chemical reactions are inhibited by products somewhat])
So how does evolution improve on this?
The most common error in genes that doesn't lead to a non-functional protein is a duplication. Lets give this two functional copies of A
So now we have:
Now we have two A's that produce D. Having two A's doesn't mean an excess of the product "D", remember D inhibits the transition of A, so overall D will be in equilibrium. Now this system has some redundancy and the cost isn't too great because excess product isn't made
With two copies of A one of them is free to mutate(Again this is seen quite often). The mutation could be anything really. Now since A(2) has changed, lets call it B
So now it's:
The chemical B could be acted on by a regulator(made by a different gene even), so this protein could become more specific. B might even have a different optimal temperature, this could also be used for regulation or it might give the organism an advantage in a different climate.( Although it's possible that B could act on another pathway but that's not important)
But what's most important is that B is another step that could be catalyzed by either organic or inorganic catalysts or regulated/inhibited.
Also now we have As and B's to transform something into D, this could greatly increase the speed of these reactions.(I could list a dozen advantages)
Lets say that any of the proteins mutates so that it is stimulated by it's own product(Simple chemistry ) Let say that B mutates to do this: I'll give it a "*" to mark this catalytic ability.
B is now able to complete this pathway even faster.(again this is quite common in molecular biology) Any A molecules
This could be favorable in many ways. But now B may be hard to inhibit. So any regulation step would be favored. Maybe B or A duplicates again(it has a history of doing this)
This process is getting really, really fast. Any A is going to be transformed really fast. We have two steps here stimulating each other. This means the two can slightly change shape to complement each other. This is an astronomical benefit to organisms that only live a few hours(see below for explaination)
Remember: B used to interact with D in the second step so a duplication should still be able to interact with B but lead to the product D. This is pretty fast but it looks like the only regulation would be when A is depleted. So any regulation would be nice because these two B's might transform A molecules that are needed somewhere else. What happens in living systems is that these two B's are free to optimize to different conditions. In one instance one of the B's might mutate to complement the other B in one condition or regulate B in another. Now that these two step have different "personalities" it's only fair to call one B "C". C now becomes a regulatory step.
Now with all these in place A,B*,C,D are free to co-evolve and adjust to different conditions. During these adaptations organisms have their chemistry change subtlety and over time both the speed and specificity can change to favor the conditions. After a while the shapes have changed and may not be able to interact with each other. The ability of C to transform into D might be only a small trickle of reactants into products unless a cyclin is present to change the shape of C into D
The end result is that this pathway is highly specific, very fast and able to be regulated at many places. Now it is irreducibly complex. More than that now this can be expanded in alphabetical order to intergrate with the whole organisms biochemical atlas at large. it could be E, F, G, H, etc. In modern organisms these biochemical steps are at some level all connected. High blood sugar releases insulin which in stimulates leptin and suppresses hunger in the limbic system.
During this process the shape of D may have changed so that A no longer activates it. One DNA base difference can cause the protein it makes to change shape. There is some redundancy if you google "RNA wobble" basically the three bases that define the amino acids that make up proteins. Slight modifications that optimize the system will be favored. In the end it is irreducibly complex because this cascade is so specific that removing any part now breaks the pathway.
Understanding the origins of these pathways is essential to understanding that they do. This is used in drug discovery all the time. These useful pathways don't have to evolve separately for each organism. The billion year passage between the earliest prokaryotes and eukaryotic cells is a long enough for these cells to accumulate these changes to build the tools needed for more complex organisms. The descendants can derive these pathways and use them for different uses. You can use a socket wrench to tighten or loosen bolts or if your clever you could use it to drive in nails. The proteins in these pathways are usually slight modifications on the proteins in front of and behind that used to have more general functions
(What I showed you is just one of a bunch of different ways these things can evolve and I'm not very good at this yet but I still know better that Michael Behe.