May issue in Delaware means that weather or not a CCDW permit is issued is up to the judge who is reviewing the application. Typically the reason for a rejection is better than "just because" as that would be tantamount to an abuse of judicial discretion and subject to a reversal of the decision. When I was with the AG's office, the most common reasons for rejection were persons having really bad driving records (multiple rather serious moving violations such as reckless driving, aggressive driving, inattentive driving, etc.), they have prior adjudications of juvenile delinquency, or they have prior non-violent misdemeanor convictions, or prior DUI convictions (first and or second offense). Pardoned felonies can also be an issue. For the most part any of the foregoing criteria would be an indication to the reviewing judge that the applicant tends to exercise poor judgment and it may not be a great idea to have them strolling around with a concealed weapon.
In regard to the "reason for applying", most will tell you that simply stating for protection of self, family and property will suffice.
