A situation or fact that means you're not allowed or able to participate in something is a disqualification. Being born in a non-US country is a disqualification for becoming President of the United States.
Not speaking French might be a disqualification for studying in France, and being over 18 is a disqualification for participating in Little League baseball. Another kind of disqualification is the action of preventing someone from doing something, often for a specific time period: "His disqualification from participating in bowling tournaments lasts until next year." Qualify, from the Latin qualis, "of what sort?" came to mean "be fit for a job." The prefix dis- means "not."