A person can reject your help without rejecting your humanity.

Turning down what you offered is not a verdict on you. People decline help for reasons that live entirely in their own situation, their pride, their timing, their need to manage this themselves, and the refusal is about the help rather than about your worth as a person. Hearing it as rejection makes the next offer harder for both of you.

When your help is refused, say that the offer stands and then let it go without a second push. Do not withdraw the relationship along with the assistance. Very often the offer is accepted weeks later, and it is accepted because you did not make declining it expensive.