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That is, indeed, the question. Many Creationists (e.g. Lee Spetner) claim that information cannot be increased by evolutionary mechanisms, and invoke their own version of information theory to "back up" the claim ... but there are severe flaws in all their claims.
I agree completely.
Probably the biggest problem with trying to apply any sort of "information theory" to DNA is one simple thing: Information requires at least one participant for which there is a context that gives the information meaning (otherwise, it's not information). For example, if I were to encode in a DNA strand the Gettysburg Address, it would only be information *in the context* of my encoding scheme; it would be random gibberish in the context of, say, cellular replication. Thus, for DNA to hold information, there must be a context in which it has some sort of meaning. If there is a God who designed life, it has meaning to that God (such as if that God declared life to have meaning, the DNA would carry information about life). However, if there was no God who created life and no inherent meaning to it, then there is no inherent "purpose" to the DNA, and thus, no more information than a snowflake contains; it is just a cycle that continues itself.
The only thing "interpreting" our DNA is the universe itself, and its laws of chemistry. Just like the snowflake, however intricate, contain no information (because it is not designed as such), the same holds true with DNA. There is no "meaning" behind it, just selective factors.
Now, while we as humans could ascribe meaning to a carrot plant (and declare it "food"), or a rock (and declare it "weapon"), that doesn't mean that these things were designed for that purpose. We are selecting specific objects out of a random dataset, and by the very process of our selection, we encode information to it. We do the same to DNA. Given a strand of DNA, we "encode" meaning into the strand in our own context. We may declare a gene to have the purpose of encouraging mitosis, or for apoptosis. Just like the carrot *was* good for food and the rock *was* good for a weapon, these genes *are* good for what we declare them for, *despite* not being created for these specific purposes. To declare that something was created *for* a purpose, one must already have the worldview that there is some sort of inherent meaning or purpose in life itself; you'll have a hard time getting a naturalist to believe that.
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