As you already know that, the Nintendo network id works for a different gaming console and it can be run online also. Please remember! There is a significant difference between the Nintendo network id and the Nintendo account.
All Nintendo familiars are having Nintendo account and ids. Unfortunately, new users have not much idea about the Nintendo account and id linking.
Generally, by connecting both things, you may increase your gaming experience. The combination of Nintendo id and account can help you get eshop funds by devices also.
Whatever! On another side lot of players want to unlink both Nintendo id/account for different purposes.
For you and me, there should be a lot of genuine reasons for unlinking Nintendo id, especially from 3ds. A lot of people want to sell their 3ds because they have to unlink Nintendo id etc.
Anyways, the reason does not matters, but the actual thing is the proper way to know to unlink Nintendo network id from 3ds.
Make sure your Nintendo network id connected with your Nintendo account in 3d already. Now, we are going to unlink your id from your account for your personal purpose.