In 2006 Hezbollah kidnapped 2 Israeli soldiers in the northern border of Israel.
Israel started an air strike against Hezbollah's stronghold in Beirut and in south Lebanon.
Hezbollah responded in missiles attacks against Israeli cities.
Israel has no interest in annexing any part of Lebanon, it just wants safety for its population.
Hezbollah wants power, and acting on Iran's behalf. Shooting rockets from within cities, buildings and schools it had shown that Lebanon's interests are not its primary interests.
When Israel withdrew from south Lebanon in 2000, the UN has confirmed that Israel has withdrew from all Lebanese territories. Shebaa farms are conquered Syrian territory, not Lebanese, but Hezbollah keeps insisting on it as the reason for its aggression against Israel.