Most of the time, you never get an answer to that question. True, the bank or credit card company can and will give you an iron clad reason that you have not been accepted, but not so much when you are dealing with actual people face to face.
Human beings tend to color the actual truth with their own biases and experiences. Each of us sees things a little differently than the rest of the world. This is not a new concept, it has been dissected and analyzed by better minds than mine, but it is still a valid and ongoing observation. For instance:
When my relationship ended, rather abruptly I might add, I asked "But why?" I got an answer. Well, I got the answer he wanted me to have anyway. He had, in his mind, created this scenario in which I was the villain and he was my unwitting victim. He tossed out accusations that I knew to be untrue because they were things I know I didn't physically do, such as cheating, as well as theories that I couldn't absolutely refute because they were more abstract and dealt with feelings or tone, such as mocking him. I know what I meant when I said something, yet he heard something completely different. In my opinion, he heard what he wanted to hear, but the fact remains that what I said was not what he perceived. His version of the truth was tailor made by him to put me in a bad light, therefore allowing him to leave me for another woman with no guilt or remorse. Was it the actual truth? Not exactly. However, my version of how things happened was totally skewed the other way, with me being the long-suffering martyr and him being the lying douche bag. Anyone watching from the outside had their own view of what the truth was as well, depending on which of us they were loyal to. So the "But why?" became a moot point, because there was no concrete reason or absolute proof for the decision.
My best friend and I recently had a falling out. We are no longer friends. When I saw things were going wrong, I asked "But why?" Her response was, naturally, completely out of sync with my view of our friendship. Again, her accusations and statements of fact were laced with untruths, but because she felt the need to justify her behavior, these lies had to become truths. I saw myself as her secret keeper and head cheerleader, never judging her or calling her to task for the stupid things she did, being her shoulder to cry on and her sympathetic ear. She viewed those same actions as conniving and manipulative, and convinced herself that I was not a friend but someone that used her. The "But why?" was again not answered satisfactorily because it was not based on fact but on perception and appearances.
I interviewed for a job recently. I was qualified, my resume said so. My "girl suit" was clean and ironed, my hair professional and my nails french tipped. I went in feeling on top of my game, personable and knowledgeable, smart and approachable. I believed the interview went well, we chatted, we smiled, we even laughed. I left the interview feeling confident that the job was mine. It wasn't. As with most failed interviews, there was no reason given for not being chosen, just a thank you for your interest but we have gone with someone else. So, when I ran into a friend of the woman I interviewed with, I asked "But why?" The reasons (according to her friend) she did not recommend me for a position in the company were all personal. I wore a red top under my brown suit, a color combination she is not fond of. I spoke using "big words" so she assumed I was talking down to her. Finally, because I was well dressed, she didn't think I really needed the job. Yep, I didn't get the job because she didn't like my color choices, was able to talk about the job using common industry lingo, and appeared too well dressed to need a job. In this instance, my "But why?" was answered with stupidity.
All these examples show how people can see the exact same relationships and interactions in completely different ways. My rejection was based on personal bias and a desire to show a different face to the world.
Everyone wants to be seen as a good and decent person. That's why we all create our own truths, our own answers to the "But why?" We must find the things we value most, and then build our version of the truth to fit the person we want the world to see. No guy goes around telling people he dumped his live in girlfriend because he was cheating, no friend says they threw away a friendship because she wanted to cause drama, no employer is going to tell anyone that they didn't get the job because that person wasn't a slob. Everyone is going to present an answer that benefits them, and in reality, one that puts the rejected person in a position of undesirability.
Asking "But why?" in the context of human interaction is a useless and discouraging endeavor, you will not get the closure you are seeking. In fact, you will most likely walk away with more questions. As difficult as it may be, because we are curious by nature, your best option is to accept the rejection and walk away. The answer to the "But why?" is never going to mesh with your truth anyway.