The idea that "there is ...no history, only biography" makes sense for two reasons. First, any one human being has only experienced a tiny part of what we call history. Although one may have learned the factual skeleton of past events, one has not experienced first-hand the vast majority of these events, and even has not experienced a similar occurrence. Napoleon's defeat at Waterloo is common factual knowledge, yet nobody today, not even a highly specialized historian can be sure what exactly Napoleon felt at the time. This over-generality of the historical picture limits one's understanding to a purely factual level. In a way, one only knows the history one has experienced, one's biography.
Second, for any individual, the evidence of the existence of past events is very weak. This is especially true for the events that one hadn't directly experienced. For all we know, the universe could have started running yesterday, and all previous history was made up plausibly to fit the current state of affairs. From an individual's perspective, this implies that more likely the world started off at one's birth, or at the beginning of one's conscious existence. This conclusion is more logical because people tend to consider their sensory input and memory fairly trustworthy. As far as credibility of information sources goes, most people trust their immediate sensory input most, then their memory and only then information received from other people.
What we call history is only the way of resolving a fundamental dispute between individuals. The dispute about when time began and what actually happened, the dispute between what's true for a person and what's fact. We are able to resolve that question and form societies by assuming some common and coherent world structure. There is no real history, except that which we are part of. The rest could just as well be a well written fiction narrative of enormous size.