In an interview published in Haaretz, Martin Kramer, an Israeli professor, former director of the Moshe Dayan Center for Middle Eastern and African Studies discussed the situation in Lebanon. He believes that:

Hizbollah's hubris has created an opportunity for Israel... Hezbollah probably believed it would score a few points in Arab public opinion by a cross-border operation, and that it would make one more incremental change in the rules of
the game. It was a strategic miscalculation...

But more importantly and that pretty much covers why this is going to carry on for a while, Kramer states

In any case, it is in the interests of Israel and the United States to deal with the Hezbollah threat now, and not later in the midst of a far more dangerous crisis over Iran's nuclear plans. So a war now to degrade Hezbollah is a shared Israel-U.S. interest, which means that Israel can wage it without many
constraints.

Moreover, with such a mandate from the US,

Ending the crisis is obviously not an end in itself. The objective has to be to reduce Hezbollah to a negligible factor in larger calculations, to degrade and deplete its capabilities, to the point where it's about as significant a constraint as the Muslim Brotherhood in Egypt or Jordan. It will take some time to reverse the years of neglect, and Hezbollah will not allow the halo around it to be smashed without fighting back. But Israel has a U.S. license to take its time now and get it right, and it would be foolish not to use it.

When asked if he expects the crisis to tear apart the “fragile fabric of Lebanese society”? Kramer’s response was

I don't know about the society, but I do expect it to tear apart the fragile fiction of Lebanese politics. An independent Lebanon is incompatible with an extra-legal, extra-territorial status for any militia. This fact could be papered over before; now it is exposed for all to see.

So there you have it, Israeli thinking. They saw and probably saw to it that their interests converge with those of the west. Iran had alienated most of the players on the international scene so much that they are all willing for Lebanon to pay the price of disarming Iran of any tools that it may use in what Kramer calls a future “Megacrisis”. Moreover, the fact that the perception everywhere is that Hizbollah answers to Iran also explains Saudi Arabia’s position of laying the blame squarely on their feet for Lebanon’s predicament.

The ball is rolling, nobody can stop it now, our civilian casualties will continue to mount and be counted as collateral and our basic infrastructure will continue to be hit, because it is terrorist infrastructure in western eyes.

But who is to blame? Who miscalculated gravely? Who gave our vicious neighbours, not only the excuse but also the necessary international support to carry out its operations in Lebanon? Obviously Hizbollah, who failed to read the situation in its proper geopolitical context and also failed to portray themselves as a purely Lebanese contender on the scene. They bullied the independence movement in Lebanon serving the interests of both Syria and Iran. They blindly aligned themselves with regional players whose international standing at the moment is more than questionable. Their strategy has not changed since 2000, and their quest to make themselves relevant may well end in them becoming less of a player...

In the midst of this struggle between a regional superpower and the proxies of another regional superpower, is poor Lebanon. Our diplomats have their work cut out for them, they have to explain, to plead and to bargain. They have to try and show that what Israel is doing is counterproductive and that such an Israeli policy is nothing more than a temporary solution, that this will only deepen the split in Lebanese society, that they are threatening the budding Lebanese state and our chances of evolving into a real democracy... But alas, the stigma associated with Hizbollah, both internally, on the arab scene and on the international scene, may well be to large to overcome.