The setting and time of the drama was during a rebellion that happened in south korea in which over 200 university students who protested against the tyrannical government of that time (approx. 35 years ago). The FL character is designed around a protester of that time and the ML is a NK spy (not 100% sure but that's probably who he is). Now here are the problems:
1) The way the NSA was depicted in the drama is a lot more human then what actually happened. Considering the fact they imprisoned and tortured over 1500 protesters and their justification is that they were suspected NK spies. The soldiers in the drama were more humane and were shown in a better light then they actually are (they were still the bad person but the difference between their portrayal and how gruesome they actually are is very different). This lead to certain right-winged organizations in SK to state "see, the dictatorship wasn't that bad".
2) A lot of people stated that by introducing a NK spy when there was none makes the government's actions seem more justifiable and shit. Point was there was no NK spy ever found and it was just a ruse to be able to kill and imprison protesters.
3) The fact that the FL's character is designed around a protester and she falls for a NK spy is really triggering to a lot of people.
Overall, the main problem most koreans have is the distortion of history that took place, especially since this isn't ancient history and that survivors of this are still alive. South koreans are known to take their history very seriously and most don't agree with the way the NSA is portrayed.