If you are writing on the board its fine, but you won’t find a reason why sitting shouldn’t be okay, when you are reading a passage or doing a conversation. If you are being forced to stand all day and teach, surely you will end up with terrible knee pain and back pain as well. Some teachers have swollen feet for weeks. Some schools allow sitting when you are not teaching, but some have in their policy that teaching should be done standing all the time.
If you complain to the director he will think you are making it up. For those who are having a terrible problem standing for long hours can consult a doctor and have them write a letter in Korean stating that you cannot stand all day. If that’s not possible then find a new job. Some teachers at hagwons took a chair and sat right in front of the students rather than behind the desk, because they were having knee problems.
Some teach by standing and moving around the classroom when they teach as it is easier to control and engage the students. You can sneak breaks by sitting or leaning on the edge of your desk. Get the best results teaching by being active in class. When the students have enough focus and energy they sit down. If you’re sitting all the time you may be marked as being lazy. The most important thing is that you are not a slave; you can eat, sit, and sleep whenever you want. Talk to them and tell them you have problems with standing for a long time and find a compromise. If they don’t agree get a chair and sit down.