Historically, there have been many kings and emperors who were not professional soldiers or strategists. Yet many of the states they headed were successful in warfare. Many of the kings or emperors were great soldiers, but not good governors; yet still the kingdoms were governed. A leader has one job, to lead. It includes taking advice from specialists and make a decision.
In representative democracy, the true job of a representative is to convey the decision making to the people they represent. This includes heeding to the advice of specialists who have been assigned to help the "people", through that representative. A representative in that case is just a messenger. A messenger does not need to understand the contents of the message.
The representative is from among the general populace and the general populace in plural is hardly specialist.
Edit(1): I understand that this situation is unforgivable. A minister of Cyber-Security must at least be used to the "Cyber" part. I actually commented because in Representative systems which I am used to, the specialty of Minister does not matter much. The minister is a part of the cabinet, which is just simple power sharing for rubber stamping the decision making process. The minister generally comes from the parliament. Its function is to legitimize a bureaucrat's decision, which the rep always does. It does not hamper the actual cyber security program (It also does not improve it at an accelerated rate, this just proves that cyber security is not a relative major priority for the current Japanese government, but that's beyond the point), which is run by specialized bureaucrats (most probably). Friendly Americans, the Minister does not hold much power, but just legitimatizes "people's agreement" to the actual officer in charge.
Edit(2): Please forgive my English! I am not a native speaker.