It's even supported by evidence. Irreducible complexity is where a certain structure is found in nature that cannot be broken down into smaller parts and still retain a function. Plenty of these cases have been found, the human immune system, and the bacterial flagellum are both examples of this. If you take one part out of either, they both become useless. How could these structures have evolved? They couldn't!
Well, the flagellum are likely to have developed from ATPase similar to those found in mitochondria, as rotating mechanisms are very rare in nature.
The problem is that you are assuming irreducible complexity based on the current form. At an earlier stage of evolution., various systems may have not been necessary, and just a useful extra. However, as evolution has progresses, the systems already in place become utilised by other systems, making them more vital for life.
For example, the nervous system could just be used to rapidly transmit a signal in response to a single stimulus when it would be beneficial to react faster than chemical means. However, as nervous system develops, it becomes an indispensable part of the species. However, if it had never been developed, life would still exist, but it would be different based on the different past developments.
Irreducible complexity is only so if the rest of the organism stays as it is and is not taken back in the evolutionary tree as well.
And after that, how can evolution create new information in the gene pool? Random mutations are damaging and are always detrimental. How can random mutations produce new coherent information.
If you type a random series of letters (perfectly random, with each having a 1 in 26 chance of appearing every time), you would not be surprised if there are a few two letter words in there, possibly a three letter word.
If you do that for millions upon millions of letters, you are forming so many combinations that there may be a few simple sentences in there. Now, if you change any random letter to any other random letter, chances are, it probably won't affect any of the words that you can find. Occasionally, it will disrupt words that you had in the string of letters. However, very rarely, it will make a change that either changes the words in the letter, or indeed creates new ones.
I hope the analogies to genetics are fairly clear. Yes, most mutations do nothing, and most that do something are bad. However, if you do it enough times, a few will work out to be beneficial, wither by beneficially changing current information or being the "last piece of a puzzle" in a start or stop codon, allowing new codes to be transcribed.
Another interesting thing is, that genetic code is in fact a code, and codes can't form in nature, the only codes we know are the ones we produce. Languages, maps, symbols are all codes, and they're all man-made; created by an intelligent force. If DNA is a code, and all codes are produce by an intelligent force, then DNA must have been created by an intelligent force.
Well, wouldn't the genetic code be a code in nature? You can't remove all examples before saying that there are no cards. Be know that the other codes were created by an intelligent force, as we have records or other evidence that we did so. You can't extrapolate from human culture to biology.