Why do historians consider political cartoons to be credible sources in historical inquiry

Because it offers the historian an objective snapshot of the public sentiment of the time, which the cartoonist (should be) distilling for their readers, according to their feelings, for mass appeal. I say objective as it is usually very easy to decipher their subjective viewpoint according to the publication. The value of this is that it is tapping into how the masses 'feel' rather than how subjective facts can be built to form historical opinion. It becomes especially valuable prior to this century, when public sentiment is harder to garner as we were less technologically advanced. 

Because often time political cartoons provided information concerning the political climate of the time.  They provided information about the attitudes of the people. Using a cartoon in addition to other historical resources provides a more clear picture of the political climate.