Israel is destroying Lebanon, because Lebanon hadn't done what Israel couldn't do.
By the way, does the government we've set up in Iraq, recognize Israel?
Does Israel recognize Palestine?
Does Israel recognize the democratically elected, legitimate representatives of those they fight?
No they don't!
The Hezbollah's History
The history of Hezbollah begins with the 1982 occupation of Beirut and southern Lebanon by Israel. Israel had re-invaded the country in an effort to control members of the Palestinian Liberation Organization (PLO) who had settled there and were carrying out attacks on Israel. In response Shi'ite Muslims with the assistance of Iranian Revolutionary Guards formed Hezbollah to combat the Israeli presence, and ultimately to assist the Palestinians in their fight for statehood.
The group began to execute a series of operations against Israeli and U.S. targets; the U.S. forces were in Lebanon as part of a UN Peace-keeping mission, and between 1983 and 1985, elements of Hezbollah attacked the U.S. Marine barracks in Beirut, car-bombed the U.S. Embassy and later attacked the embassy's annex.
The bombings forced a withdrawal of the western forces and civil war between various Christian and Muslim factions, along with Israeli and Syrian fighters, continued in Lebanon for several years. Hezbollah continued its attack on westerners, most notably the kidnappings of American, British and French citizens throughout the mid-1980s. The last western hostages were release after the end of the Civil War in 1992.
In 1989 the Lebanese parliament accepted an Arab-brokered peace accord for national reconciliation, and Syria assisted Lebanon's national army to control the country's various factions. The activities of Hezbollah, which Syria had used as a proxy in its efforts to combat Israel, were momentarily put in check, but the group had built cultural and political institutions that would insure its survival into the post-civil war era.
In recent years the group has focused its attacks on the Israeli Defense Forces (IDF) and the South Lebanon Army (SLA), an armed group allied with the Israelis that has greatly damaged Hezbollah's armed forces. Hezbollah efforts to end Israel's occupation, which included several well-publicize kidnappings in 2000, paid off as Israeli forces withdrew to the border in the summer of 2000.
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http://www.military.com/Resources/ResourceFileView?file=Hezbollah-History.htm