Banal human arrogance.
rdgrad15, will you let us know how you're going to handle these people you speak about after hearing some thoughts on this thread?
I don't think you need to be too kind in response to the person who doesn't take no for an answer.
- A genuine sense of superiority and grandiosity
A person may have gotten good feelings about him or herself from being praised indiscriminately throughout his/her childhood, especially when they were taught to do good things by helping other people. As adults they can only feel close to people who admire and praise them. They are simply not interested in what your explanations might be, because they believe they can help you and crave those deep programmed praise signals from outside of themselves.
So how do we handle these individuals? One could try to be stern and assertive, so not to cater to their needs unless we absolutely have to. You could offer any short answers, they could stay polite as you've been handling it, and maybe you could add 'I need to leave but would be happy to accept the help when I really need it.', you could shake their hands too and get ready to leave, 'I'd be happy to listen to why I need to accept the help that I don't need, but I must leave.'. I hope you get the drift, this is one psychological way to deal with these insecure people.