I'm sure most people are aware that Spartan society was extremely militaristic and brutal to men.

Boys were taken from their mothers at a young age and were thrown into the wilderness to survive on their own. And that was just the start of their training. Which all men, including royalty, were subjected to.

Here are a few excerpts from The Privileged Sex (a good book about stuff like this) that I found interesting.

The brutality of military training:

So rough was the Spartan agoge, or education course for males, that Artistotle thought it was more suitable for beasts than for men.

Inheritance and property ownership among women:

In Sparta, if Aristotle and after him Plutarch may be believed,[480] so many men were killed in war that heiresses were numerous and extremely powerful. By the 4th century B.C women owned two-fifths of all public land and a major proportion of private land as well. When Spartan mothers demanded that their sons return from war, either with their shields or on them, they may have been motivated by more than pride alone.

And the lifestyle that Spartan women enjoyed:

In neither Athens nor Sparta were upper class women expected to work.[943] In the latter, so crass was the contrast between the “Spartan” life of men and the luxurious ways of women that Aristotle blamed it for the city’s decline.[944]

The sources that are cited are,

Aristotle, Politics, 1270a 23-4
Plutarch, Agis, 7.3-4.

And a contemporary source,

Pomeroy, Families in Classical and Hellenistic Greece, p. 54

I was able to find Plutarch's Agis online here:

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Agis*.html

There are a few passages that hint at the drastically different lives that men and women led but probably the most direct are these two:

Therefore, even before he had reached his twentieth year, and although he had been reared amid the wealth and luxury of women, namely, his mother Agesistrata and his grandmother Archidamia (who were the richest people in Sparta), he at once set his face against pleasures.

And:

The women, lifted up by the young man's high ambition, were so changed in their purposes, and possessed, as it were, by so great an inspiration to take the noble course, 3 that they joined in urging and hastening on the projects of Agis, sent for their friends among the men and invited them to help, and held conference with the women besides, since they were well aware that the men of Sparta were always obedient to their wives, and allowed them to meddle in public affairs more than they themselves were allowed to meddle in domestic concerns.

Now, at this time the greater part of the wealth of Sparta was in the hands of the women, and this made the work of Agis a grievous and difficult one. 4 For the women were opposed to it, not only because they would be stripped of the luxury which, in the general lack of higher culture, made their lives seem happy, but also because they saw that the honour and influence which they enjoyed in consequence of their wealth would be cut off.

According to the above, women had more wealth than men, lived easier lives, and even had their own political power that was exclusive to them. They then used that political power to encourage men to sacrifice themselves so that women could continue living the lives of luxury that they were already accustomed to.

Does that sound like a society where women didn't have any rights or were oppressed? And what about men? What rights did they have?

If you were a man, you could have been king if you were lucky. But then you'd have to lead your army into battle and do all that kingly stuff while your wife stayed home and enjoyed the fruits of your kingdom. So maybe becoming queen would have been a better aspiration for a Spartan. Or just a regular woman since they seemed to live pretty easy lives regardless of their social class.