Will X means
X is expected to be true or happen in the future,
and will does not provide information any state of desire, need, correctness, or ability, though ability is implied (generally you will not do something you cannot).
If you want to say "X needs to happen", you likely want to say must X.
Understand that must X is not synonymous with need to X - must X really means "X is required" - and that requirement typically comes from logic/deduction (diameter must be 2 x radius, Mary must have been here because she left her jacket), consequences (I must eat to avoid hunger), or authority (you must turn in your report by today).
If none of those apply just use the word "need". Must need X is also possible.
I would eat but I didn’t eat.
When we get to the word but, at that point in the sentence, we already know you didn't eat. Speaker/listener is expecting the reason why you wouldn't eat after but.