Yes, this will win public support against the Army's offensive.
It's a question about cost benefits.
The people lose faith in the institutions, the state lose support and people become afraid to send their children to military run schools. The Taliban think the benefits of this are bigger, than the negative PR and hostility they get for the act.
... and here's the thing, they may be right, the government incompetence in dealing with them, may make the people more afraid of going against Taliban than going against the government, and that's fundamental how a state function, people have to fear the retribution of the state more than they fear non government groups like Taliban, if they doesn't, the state's institution becomes powerless.
