You don't understand because you're understanding it wrong. You're trying to find a word for word substitution. For nouns, yes, that could work; but for verbs, you have to understand its meaning first in order to be able to translate it to English.
会 has to 2 common usages.
1. Expresses one's ability.
2. Expresses one's intention.
You were confused about the 2nd usage, that's why I didn't even touch on the 1st one. Let me explain the 2nd usage even more literally.
I don't intend to go to the hospital tomorrow.
Now, from my translation, you tell me, in English, is that a "won't" or "can't"?
If you wish to express "I won't go", you say "我不去"。
If you wish to express "I can't go", you say "我不能去", "我没办法去"， "我去不了"
Now, do you need me to explain "2. 他今天晚上会来吗？" as well?