Just realized I didn't explain the connection.
The "must" is implied. This construction *means* must/to have to do something.
Eg. Ginkou ni ikanakute wa ikemasen. It is no good if I do not go to the bank.
If its no good if I don't go to the bank, then I must go the the bank, right?
Ringo o kawanakute wa ikenai. It's no good (if I) don't buy apples, therefore, I have to buy apples (in order for it to be "good").
Kusuri o nomanakucha naranai yo! I can't resist taking my medicine, therefore, I must take my medicine.
(this is literally a double negative: Not taking my medicine is irresistible, which doesn't make sense, since not taking medicine being irresistible means that taking it is resistible, hence negating the "must" aspect. Think of it more as "must not do" as in, (I) must not do the act of not taking the medicine, which makes more sense)
Benkyou shinakute wa ikenai. It's no good (if I) don't study, therefore I must study.
Another thing, in informal conversation, you can drop the "ikenai, etc.", so "ikanakucha" infers "I must go", just by itself. Tabenakucha>I must eat.., etc.
I hope this finally clears this up.