Hope you understand my English...
'는' give a hint there will be more sentence/meaning
For example,
1. 난 널 미워하지 않아
I don't hate you
2. 난 널 미워하지'는' 않아
I don't hate you, (but.... )
1-a. 난 널 죽이지 않을꺼야
I'm not gonna kill you
2-a. 난 널 죽이진(지는) 않을꺼야
I'm not gonna kill you.. (but....)
As Chaeyun said, there is no problem if you don't use '는'. but you can use '는 않다' when you give a hint or there will be a twist ( like twist of movie )
Native Koreans can guess/expect there is something other than the first sentence with '는'