It's all about power.
The objectives of the two sides vary greatly. For Israel, it's a war for peace and stability. All the Israelis really want is to be left alone, to live in peace. For Hezbollah, for all Arabs, the single goal is the raw exercise of power.
Hamas captured a young Israeli soldier to force Israel to release dozens, perhaps hundreds of terrorists that can be used to continue to fight Israel. Hezbollah used the same tactics, plus rocket attacks to terrorize Israeli civilians, to force Isreal to release several Hezbollah terror experts. Both ploys failed because Isreal had decided such a deal would only lead to more kidnappings, more terrorism, and more deaths. Israel fought back, and the Middle East is once more embroiled in war. Hamas and Hezbollah both misjudged Israel, and failed to understand that the power to cause a pinprick wasn't necessarily enough to keep Israel from fighting back.
Power is all-important in the Arab mindset. It's the most important thing in their existance. The exercise of power is implicit in everything an Arab does, from birth through life to death. The addition of another child is seen as an extension to the power not only of the parents, but of the extended family, the clan, tribe, nation, and people. The lust for power determines what education a child gets, whom they marry, where they live, and what role they are given in life. It's inherent in their social, cultural, political, and economic life. Power is everything, even their religion. Islam is a "religion" steeped in the exercise of power, to the exclusion of all else.
In Lebanon, the local elected government is weak. Thanks to the help of Syria and Iran, Hezbollah is powerful, especially in the south and east of the nation. Hezbollah, a terrorist organization with little political support outside its areas of operation, exercises power that otherwise would reside with the elected government. Hezbollah, in an exercise of raw power, started a war with the sovereign state of Israel from Lebanese territory. Their exercise of power led to a major war that threatens to totally destroy Lebanon as a sovereign state.
Israel has made little progress in reducing the power of Hezbollah, because they have tried to fight this war while remaining in the "good graces" of the United States and Europe. This is a fallacy. The United States will continue to support Israel, but Europe has shown its true colors - its anti-semitism, its fear of the exercise of power, its fear of losing a "moral superiority" that doesn't exist. The only way Israel can win is as it's done in the past - the use of overwhelming power and force against a numerically superior enemy. The only thing Arab armies fear is greater power than theirs. The only thing that can win against power is greater power. Thoroughly destroying Hezbollah is the only way Israel can gain a victory over that terrorist enemy.
The same can be said about the war against Islamism. The West must understand first that Islam is a religion of power, based on power, and sustained by power. Once its power is broken, Islam will disappear, shown to be the sham that it is. Everything about Islam is about power, from Mohammed being proclaimed the "last prophet" (a blatant, bald-faced power grab from God Himself), to the fact that Islam is spread by force, rather than by persuasion, to the fact that anything is permissible against the "infidel", which is anyone who isn't a muslim. Power, pure power, and nothing but power. Without it, Islam would be a farce.