Typically, the lender will send you a notice of denial. This letter should include your rights under the Fair Credit Reporting Act that you are entitled to know why the denial was issued. However, the burden is upon you to make the request which is usually within sixty days of the denial of credit.
Send a letter to the company that denied you credit and request the reason why. They are duty bound to provide you with the reason for the denial. If they do not, then this is potentially a violation of the FCRA.
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This previous answer assumes they looked up your credit report. They may have used a service that lists people who do not qualify for credit based on past defaults. If the company used internal information to their company and did not access your credit report then they do not have to tell you why they denied you even if you ask them.
Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship.