Is our genome decaying (see "Genetic Entropy"), and, if so, is this evidence for our genome being "young"?
If I understand the question correctly, you are asking why random mutations (most of the non-silent ones are deleterious) cannot create information and improve the overall fitness of the organism. 

This is a common creationist statement, and has been shown to be incorrect in many different ways. The best way this can be shown to be false is by simply applying natural selection. 

E. coli has a beneficial mutation rate of $10^{-5}$ per genome-generation (source) and a detrimental mutation rate of $2×10^{-4}$ per genome-generation (source). 

Therefore, at first glance, the claim that the "genome is deteriorating" appears plausible. However, natural selection quickly acts on these mutants with deleterious mutations due to their low fitness. Therefore, the deleterious mutations are removed from the gene pool and are replaced with their beneficial counterparts instead. 

If we define "information" as beneficial adaptations to the environment, random mutations themselves do not directly create the information. It is the application of natural selection that allows the fitness of the organism to increase despite the presence of random mutations.