While I am not too familiar with a primary secular reason, the main religious reason stems from the Bible itself.

Satan is referred to as a "dragon" in the book of Revelation, chapter 12. In particular, verse 9 identifies Satan as "the great dragon...the original serpent, the one called Devil and Satan, who is misleading the entire inhabited earth; he was hurled down to the earth, and his angels were hurled down with him." (NWT 2013 Revision)

It is important to note that the dragon in this case stems from Greek mythology. The apostle John was the writer of this book and was imprisoned on the island of Patmos, near Asia Minor, in the Aegean Sea, which is in the vicinity of Greece. The Greek word used in Revelation for dragon is "dra'kon".

In Greek mythology, the dragon is appears regularly. Flavius Philostratus discuss dragons in the land of India in The Life of Apollonius and they are again mentioned in the Greek epic Argonautica, book 3.

Often enough, these dragons are said to be "serpent-like" in appearance, such as with the Ladon. And it is interesting to note that John also describes Satan as having "seven heads", which is a symbolic use of the number 7, but coincides with Greek descriptions of some dragons, like the Ladon, which had multiple heads. Since Satan is considered by a number of people to be the "original serpent" that misled Eve in the Garden of Eden, the description of a serpent-like dragon, along with its other features, in combination with the use of the actual term "serpent" in Revelation, makes sense that a "dragon" is an appropriate picture. Dragons were seen as destructive monsters, ones who caused terror and fear and had great power. Thus, it is no wonder why John was inspired to use the monster "dragon" as the beast to describe the most wicked adversary of God Almighty when recording what he saw in his vision.

Edit: some words