The "no new information" argument probably requires a creationist background. It is, after all, one of the most common creationist deceptions. It typically relies on introducing no measure of information at all, which reduces the whole thing to meaningless rhetoric. If asked for a measure - which is required make the argument meaningful the typical answers is evasion and refusal.
Another argument is to say that natural selection reduces information - which can only be true if information is measured by genetic variation in the gene pool - and then turn around and say that mutations cannot increase information. Of course, any novel variant would represent an increase in diversity - in the same way as the elimination of a variant is a reduction. The two statements simply cannot both be true if a consistent measure of information is used.
Creationist Lee Spetner did do better. But not much. In fact he introduced several measures changing the measure to get the answer he wanted each time. Since different measures of information can give different results (and because we know that Spetner changed the measure to avoid admitting to an increase at least once) it cannot be said that this version of the argument is any more honest.
Of course, mutations can and do increase the diversity in the gene pool and duplication and diversification can increase the information in the genome. The latter is where an additional copy of a gene is produced and one of the two copies later mutates. Duplication is usually dismissed on the (incorrect) ground that an extra copy adds no new information (the presence of the additional copy is itself information) - but even if this is accepted mutation to either copy must add information since the two genes are no longer exactly the same.
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