E.g. a very rich and fortunate person offers you to use any amount of his wealth, however, either by or without saying, you will never want to use that person's money.
One phrase often used in English is that of being "too proud" to accept help. I might offer a friend some assistance, but notice that he seems to feel a bit of shame that he needs help. When I get home, I might have this dialogue with my wife:
"So, did you buy him any food at the store?"
"I offered to, but he was too proud to accept the help."
proud (adj.) having or showing a consciousness of one's own dignity : I was too proud to go home.
On the other hand, maybe it has nothing to do with such pride; maybe you simply have a moral disagreement with the person making the offer. For example, suppose I need some help at Christmastime, and a friend of mine offers to give me some money, but I know this person is a drug dealer, so I don't want to use that money. In this situation, we sometimes use the expression tainted money (or ill-gotten money). Again, a conversation with my wife:
"Tony offered to give me $300 to help with Christmas."
"Really? Did you take it?"
"No, I didn't want to accept any of his tainted money."
tainted (adj.) something that is tainted is spoiled by an unpleasant feature or quality that often makes people not want to be involved with it : tainted money
I agree with J.R.'s answer: pride is indeed a good word.
However, I'd like to suggest another word, dignity. According to your comment, I would say that he is a man of dignity, and he appears to stand on his dignity.
From Oxford Dictionaries Online,
NOUN (plural dignities)
1. The state or quality of being worthy of honor or respect:
'a man of dignity and unbending principle'
'the dignity of labor'
stand on one's dignity
Insist on being treated with due respect.