They have the support of most shia muslims, a lot of sunni and about half of Christian Lebanese.
People also claim that Hezbollah brought destruction to Lebanon by inciting Israel. The kidnapped soldier was used to free muslim prisoners in Israel. Hezbollah has 1 Israeli soldier while Israel has thousands of Palestinians held prisoner.
Israel did not achieve its objectives in the 2006 Hezbollah-Israel War, therefore making them the losers in the war.
Also seen by many muslims as the only thing stopping Israel from taking more land.
Lots of propaganda is also made against them, mostly by violent Zionists out to kill innocent people
Answer: Hezbollah fights to stop Israeli agression and one day remove the Zionist State of Israel in Palestine and to return the over 5 million Palestinians refugees their land in Occupied Palestine. They do not use suicide bombings, and condemn the killing of innocent people.
2) Not true, Israel is attacking innocent children, many times with unguided missiles. What makes the Israeli state any less of a terrorist organization than Hezbollah?