Ultimately, Touma doesn't want everyone to know about the truth of Academy City, where corruption prevails and everyone is just a test subject. If everyone knows the truth, all chaos would break loose.
And once people learn about magic, the domino effect happens.
People learn about magic -> People learn about the struggle of power (Science vs Magic) -> People learn that Academy City is corrupted beyond belief in every aspect possible -> A big war ensues where everyone chooses a side
Just think about the magic side as a gang that is trying to take control of the government. The government (Academy City) has been sweeping their own dirty deeds under the rug, as well as concealing their opponents. Learning about magic opens the door to everything.