As for me personally, I have a piece of paper from a University that says I'm a historian. So that's simple.

Reading a lot of other secondary works (written by historians who read a primary source, i.e. a historic text) is what historians do most of the time. The core issue, I would say, is that historians approach a primary source differently than a layman would. For the layman, a letter from a poor peasant to his lord asking for tax relief because of a bad harvest would be primarily that. The historian approaches this source with a different mindset, first formulating a question - "How did the relationship between peasant and lord look like from the peasant's perspective?", for example. Then they would place the source in a wider context, compare it to other sources and use it to craft a narrative, which they place in the context of other historical research ("Contrary to the works of Eisenengel, MA, peasants were very much willing to pay taxes and only tried to get them reduced if it was utterly impossible to pay them. Another example of this is in the records of the Duke of Someplaceorother, who noted that on occasion peasants paid higher taxes than they were required to.")

Carlin lacks (I presume) the training to do this, which is mostly knowledge on how certain historians have approached a topic, and what methods and questions have not yet been applied to a source. I would also guess that much of what historians do isn't really all that interesting to the average history enthusiast. It is very much a look at tiny details that create an overarching picture, and a good historian will always make sure he painstakingly references those details and doesn't overreach. If you want to produce an overarching narrative that fits into a podcast episode, you can't really use primary sources and have to rely on secondary literature.