Well, I said it is fallacious, but your assertion goes too far. For example, there is a remote analogy between computer programs and expression of DNA. For another, there is an analogy between DNA transcription and information encoding. For another, we often speak of "biological clocks" which is an analogy.
nor is there anything designed by humans remotely similar to living processes
I guess you must disagree, but I consider the products of genetic and evolutionary programming techniques to be (human) designs because their functions satisfy a prior specification. These techniques are very similar to biological evolution.
But the main reason why it is hard to believe is that ID advocates are such cruddy liars.
Every last one of them? I think you need to distinguish between error and lie. Most of the anti-evos who post here are simply ignorant.
There is absolutely nothing designed by humans that looks like life. There are a few atttempts to copy the mechanism of evolution in computer programs, and some of these are commercially useful. The model they follow, however is stochastic variation and selection.
Life is messy, brutal, wasteful, painful and remorseless. If a human designed anything with the attributes of our ecosystem, he would join Hannibal Lector in the plexiglass cage.