Why did so many people in europe and north america support the revolution of greek
nationalists against the ottoman empire

Many people, notably the Europeans, especially the Russians and the British were worried about the Greeks in the Ottoman Empire. One of the reasons, for the Russians at least, was that both Russians and Greeks are Orthodox Christians, so they were very touched when the patriarch was hanged. For the British, they felt the status quo and the peacefulness of Europe should be kept and they did not want to disrupt this general quiet time in Europe. They equally wanted to keep the Concert of Europe, which was a time period where power was balanced in Europe.