The conventional wisdom holds that any military action is counterproductive. The doves point out that the Israeli counteroffensive has boosted Hezbollah's standing in the Arab world.
Well, sure. But Hezbollah's prestige was also boosted by Israel's 2000 withdrawal from Lebanon. If aggressive Israeli actions boost Hezbollah, and conciliatory Israeli actions boost Hezbollah, then maybe Israel's actions aren't really the prime mover here.
The Israelis cannot win, in the court of world opinion. They cannot depend on anyone else but themselves. World opinion right now is devoid of insight and understanding. So, for Israel to try and court the world's approval is certainly not in their best interests.
Certainly, Hezbollah is not going to stop just because the Israelis call off the charge. They don't want Israel to call it off.
Why? For many reasons that I could list. But the one that doesn't get a lot of mention, is recruitment. The more there is a cause, the more they can convince people to take up that cause. The more people that take up that cause, the more expendable fighters, in reserve for worldwide jihad. The pathology of the jihadist movement may be complex. But when you look at it closely, it is quite predictable.