Yes, "It would be a great mistake to argue that Art and Music should be optional/should not be compulsory subjects" is natural English. In the United States optional courses are called "electives" so one might say "It would be a great mistake to argue that Art and Music should be electives." "Argue" has a range of meanings. It can refer to a spirited but polite intellectual discussion. "They liked to argue for hours about Keynesian versus Hayekian economics." A single person can "argue X," or present an "argument for X," which means a civil, polite presentation that gives reasons to believe that X is true. There is an adjective, "arguably," which means that the speaker doesn't believe something but acknowledges that it could be true. "Arguably, Pluto should be considered a planet after all." There is also a second range of meanings in which an "argument" means an angry dispute, a row, an altercation, a quarrel. "We were enjoying our dinner when the couple at the table next to us suddenly began to have a loud, heated argument. It went on and on until eventually the maitre d' asked them to leave."

Yes, you are right. To argue can also mean to give the reasons for your opinion, idea or belief. Your example is perfect for using argue in this manner. Excellent!

Hi Tania, As you've alluded to, to argue something is not always equal to what most people consider an argument. It can be a civil discussion where you need to state your case for something or you can use it to negate someone else's reasoning as you have done in your example: "It would be a mistake to argue that Art and Music should be optional subjects" "I would argue that it is very important that Art and Music are compulsory subjects" "They argued at great length over the requirement for Art and Music to be compulsory subjects"