It is a little odd for an instructor to ask you which aspects of the past appeal to you personally and then to tell you not to consider modern sensibilities in your answer. It is surely impossible to say what appeals to us without in some way consulting our own values which are grounded in our own time.
That said, let us look at some aspects of Spartan life that do and do not appeal to me. The idea that the Spartans would keep a whole “race” of helots as slaves does not appeal to me. It is true, of course, that many societies in the ancient world had slaves. However, this does not seem to me to make it right for them to have done so. I also do not really approve of the Spartans making their entire society so militarized. This does not seem to have been necessary since many of their fellow Greeks lived in societies that were not like this.
I do admire, however, the Spartan insistence on dedication to their state. The Spartans essentially centered their lives around the needs of the community. It is admirable, in my mind, that they were so selfless.
Thus, I do admire the Spartan selflessness, but I do think that there were some distasteful aspects to their society. I must admit that these perceptions are probably colored by the time in which I live.