Both type of sources have their uses in different situations. If I am writing about monks in the early middle ages, I need to do two things: look at the primary sources written by and about monks, to get a sense of what contemporaries thought about them, and to look at the secondary literature, to get an overview of what previous scholars have thought about this topic. Modern academic historians build upon the work of others, since even the most obscure topic needs to be viewed in its context, and that means looking at other history books.
Moreover, all primary sources are biased. This is not a bad thing, since bias tells us a lot more about history than a bare narrative of facts, but it does mean that we need to read every source carefully. When a primary source tells us that A did B , it does not mean that A actually did B or that B happened in this particular way. Previous historians have often analysed the evidence and produced arguments about what they think the interpretation of the source should be. Even if we disagree (and I personally am very wary about any book published more than two/three decades ago), we will need to read the older secondary literature in order to understand their arguments, then refute them with a combination of primary and secondary sources.
This is slightly different for members of the general public. I am not sure starting from primary sources is the best way forward, especially for ancient and medieval authors. These writers lie, exaggerate and fulminate again their enemies. This is sometimes very obvious, but often it is not, especially with sources that are seen as the 'classics', such as Livy or Herodotus. This is especially obvious with the Byzantine sources I'm familiar with, such as Procopius, Michael Psellos and Anna Komnene. Scholars have literally spent decades if not centuries arguing about what these writers were trying to say and it is clear that their image of the sixth/eleventh/twelfth centuries is very distorted. After all, each source at best only represents one perspective and they are often not works of history as we think of it, but works of literature. This is why I often recommend recent secondary literature instead to newcomers to Byzantium, since they have at least attempted to synthesise all the recent developments in academia and thus provide a reasonably accurate narrative, whereas the sources themselves don't.