South Korea has never had a good track record when it comes to conscientious objectors. A year in jail might seem preferable, but in the past employers could see if a person had been convicted and imprisoned and this greatly reduced employment options. I don't know if that's true today, but the social stigma can be great.

In fact it's only been recently (2018) that the SK Supreme Court ruled that being a conscientious objectors wasn't a crime, and is justifiable grounds to refrain from military service. Prior to that the only recourse for objectors remaining in Korea was jail time, often with punitive sentences double the length of required military service, or even longer. (I'm familiar anecdotally with one instance where an objector was sentenced, imprisoned, and upon release was drafted again, sentenced and re-imprisoned, and subjected to this treatment for over ten years.) When it comes to human rights SK is slowly improving, but it is not anywhere near Western European levels yet.

I'm sorry you have to deal with this as well. Remain true to your convictions, yours may be the case that changes your countries laws, and if not, you will keep your personal integrity