As you noted, your answer is that
The Greeks were the first people to study history in a organized manner.
Allow me to explain a bit, for teaching purposes.
Herodotus (about 484-425 BC) is known as "the father of history," because his writing pioneered the field of historical research. Indeed, we get the word "history" from him. He called his writing about the Greeks and their wars with Persia the ἱστορία (historia), which in Greek meant "investigations." We now call his book The Histories, but it could be called "The Investigations." In doing his investigations, Herodotus payed attention to all sorts of sources -- myths, legends, oral histories, his own observations, etc.
The second generation of Greek history-writing featured an even more organized and thorough researcher, Thucydides (about 460-400 BC). Thucydides' History of the Peloponnesian War sought to be as fair and objective as possible in his account of what happened in the conflict between Athens and Sparta.
The ancient Greeks essentially began the field of history writing (historiography) in the way that we think of that subject today.
