Some years ago a friend of mine told me that his professor stated that Sparta had to protect itself from other greek countries, and that's the reason why we normally associate Sparta with militarism, althrough we usually see it as an offensive force rather than a defensive one. How true is that?
http://www.ancientmilitary.com/spartan-military.htm
Sparta was known for being the only Greek city without a city wall, a famous saying among Spartans went something like, “Our men are our walls.” - On Sparta' by Plutarch; Spartan quotes
Right of the bat, this denotes that if it was a force devoted to defence, then there would be a wall, certainly if facing external threats.
During the first year of my degree in History, we actually focussed on the Ancient Greek military. One thing that was suggested by my lecturer was that one thing they had to internally defend against was the helots that they had enslaved. There were a handful of revolts in the past by the helots; 5thc. BC (Pausanias), the massacre at Cape Taenarus pre-464 BC earthquake, the 464BC quake and then during the Peloponnesian War. It was during the Corinthian War however (395-387 BC) that the helots gave a 'one-two' punch or were part of one, by uprising after the Spartans had fought Epaminondas of Thebes - and had lost a lot of fighting men in the process.
This internal defensive methodology comes from the fact that they were slaves subjugated by the Spartans. According to Herodotus, this was in particular after the Messenian Wars, with most of the helots being derived from those people. Antiochus said that "those of the Lacedaemonians who did not take part in the expedition were adjudged slaves and were named helots". The word itself comes from halískomai, "to be captured, to be made prisoner".
So it makes sense that given how the Spartan population itself was quite small compared to the population of people that they had defeated over the years, that they had to defend themselves internally as much as they did externally. Although I would argue that they were solely militaristic because of this, but stating that I think it was one of the many defining factors.
Offensive -
ca. 750 BC, subduing Amyclae and Laconian settlements, 1st Messenian War
669 BC, Battle of Hysiai - but this led into a Messenian uprising for 20 years, so, offensive followed by defensive
Arcadia
Cynuria - 546 BC
Defensive/Defeats -
Sphacteria in 425 BC; unit surrender following a more isolationist practise post-Persian invasion
Corinthian War
Battle of Leuctra
When reading around the other factors that went on around these events, other factors such as becoming more isolated, having a low birth rate and the introduction of commercialisation outside of their iron bar 'currency' began to change their society and how they operated. While this applied predominantly to the warrior caste, it is the warrior caste that the military [and the question] focusses on.
Sources
Thucydides. The Peloponnesian War. London, J. M. Dent
Geography Trans. by H.L. Jones (1924)
Military Theory and Practice in the Age of Xenophon, By John Kinloch Anderson
Spartan Society: Structural Ritualisation In An Ancient Social System, J. David Knottnerus and Phyllis E. Berry; Humboldt Journal of Social Relations, Vol. 27, No. 1 (2002), pp. 1-41
Holland, Tom. Persian Fire: The First World Empire and the Battle for the West.
P.S I actually did an essay that would have been very useful to help me answer this, but sadly all of my degree essays were lost during a wipe to fix some broken software a few years back, and I don't have anywhere near all of my old books at my boyfriend's house on the matter.
You can refer to this post, courtesy of u/Iphikrates, for discussion about the process and reasons for Sparta's transition to such a militarized state.