The High Sparrow came from a background of affluence. He found peace and fulfillment through austerity and self-denial.
Since so many others appeared to be helped by his message, it would be reasonable for him to conclude that this is the remedy Westeros needs.
Loras, Margery & Cersi needed to be shown that they were no better than anyone else. Taking them out of their safezone would be the fastest way to reach them.
To me, his methods made him no better than them. He was just another tyrant, clothed differently.