To disqualify someone is to not allow them to participate, or to make them unfit for participation. Turning eleven would disqualify a person from playing on a soccer team for kids ten and under.
Judges will disqualify a marathon runner if they discover she's actually wearing roller skates, and a baseball player's age may disqualify him from playing on a certain team. Being blind disqualifies people from driving, and a criminal history can disqualify someone from working at a school. Disqualify adds the "do the opposite of" prefix dis- to qualify, which comes from the medieval Latin root qualificare, "to attribute a quality to."