The creationist "information argument"....

It seems to me like the most popular creationist argument against evolution is the claim that "mutations can never add new information to the genome." Answers in Genesis uses this argument, the ICR uses this argument, and they seem to think that it is proof that "molecules to man" evolution is impossible. They say that all observed mutations either change the information or delete it.
While debating another creationist at another message board, the creationist tried to use the sentence "I like food" to prove that mutations can never add new information to the genome. His argument went something like this:
I like food.
I like food. I like food. (Copy mutation, no new information.)
I like. (Deletion mutation, loss of information.)
I lkie food. (Rearrange mutation, loss of information.)However, the creation information argument seems to me to have one fatal flaw: the ability for multiple mutations to add information.AGTCAAG (original genome)
AGTCAAGAAGAAG (a few copy mutations)
ACTCAAGATGAGT (A few point mutations)We have the original section but a completely new one has been added. Is this not new information?The creationists seem to have overlooked the ability of copy mutations + point mutations to generate information.Another example:
Pretend that we had a gene that made a certain protein. Pretend that there was a copy mutation, so now we have two copies of this gene. Pretend that one of these copies had a few additional point mutations. A lot of things might happen, but one of the possibilities is that the new, slightly different gene would produce
a new, slightly different protein. A new gene and a new protein would have been created. Is this not new information?Yet another example:
Let's pretend I am the owner of a company that makes toys. I tell Mr. Bob to send a letter to Mr. Fred telling Mr. Fred to make a stuffed cat. However, Mr. Bob isn't paying much attention when he's typing up the message and he accidentally copies my message twice.Make a stuffed cat. Make a stuffed cat.Mr. Bob sends the message to Mr. Fred. Mr. Fred reads it, copies it, and sends it to the toy-making factory. However, in his letter to the toy-making factory he accidentally changed one of the letters.Make a stuffed cat. Make a stuffed rat.The toy-making factory makes two things: stuffed rats and stuffed cats. New information has been added, and the new information told them to do something new. Let us also pretend that the stuffed rats were amazingly popular and I got rich. This would be both new information and beneficial information (for me and my company, at least), right?I was able to add new information to the "genome" by simply doing the stuff mutations do: copy, add, delete, and modify.It seems to me that the creationist information argument is bogus.