If a person needs help but will not ask for it because they don't want to need to depend on other people (based on their pride), is the word hubris fitting to describe this?
How would you use it in a sentence for this situation?
Hubris refers to a belief in one's infallability, or inability to fail, not just pride.
If someone refused help out of a belief in his/her "infallability," that would be hubris.
If someone refused help out of "pride," knowing full well s/he could fail, that would not be hubris.