忙しくない = not busy 忙しくはない、、、 でも/しかし私はほかにやらなければならないことがある= I'm not busy but I have to do something. When you want to do something, you can use 忙しくない for reason to take part in something. A「How are you? Are you free this weekend? Shall we go to a theatre?」 You「It sounds good. I want to join that because I'm free this weekend.」 When you don't want to do something or don't want to take part in something, you can use 忙しくはない to excuse yourself. for example A「How are you? Are you free this weekend? Shall we go to a theatre?」 You「I want to join that, I'm not busy this weekend but I have to do something so I can't join that sorry.」 If you didn't understand please ask me.