The military operations were legitimate as Israeli self-defense:

The military operations were a legitimate use of the Israeli state’s right to defend itself and its citizens: To quote then-President-elect Barack Obama - "If somebody was sending rockets into my house where my two daughters sleep at night, I would do everything to stop that, and would expect Israel to do the same thing."(1) Prior to Israel's 2008-2009 military operations, Hamas had consistently violated the terms of the ceasefire between Gaza and Israel. It launched a total 6,300 rockets during an agreed hiatus in the confrontation, killing 10 and wounding more than 780. Hamas refused to extend the truce past 19 December 2008 and subsequently resumed attacks, firing nearly 300 more missiles, rockets and mortars.(1) Hamas was the first to actually escalate the conflict after the ceasefire expired, with a systematic increase in rocket attacks to a magnitude of hundreds of rockets fired daily in late December.(2) The 250,000 Israelis who lived in the southern part of the country were under constant threat, often in bomb shelters, and the economy suffered as a result.(1) Israel went to great lengths to avoid its military escalation. Just a few days before Israel's military operations, outgoing Israeli Prime Minister Ehud Olmert made an appeal on the Arab television station Al-Arabiya asking Gaza residents to stop the firing of rockets and mortar shells so that a military response could be avoided.(3) This appeal was apparently ignored by Hamas and the other militant groups in Gaza, and so Israel proceeded to respond militarily to remove the capacity of Gaza to launch rocket and mortar attacks  – Israel was left with no other way to ensure that the inhabitants of the country’s southern regions would not have to live in fear of rocket fire.  Gaza was also a test case, intended to prove that Israel remained a legitimate and authoritative actor in the region. Much more was at stake than merely the military outcome of Israel's operation. The issue, rather, was Israel's ability to restore its deterrence power and uphold the principle that its citizens cannot be targeted with impunity.(4) Israel's military operations were a good tool to fulfill this need for self-defense and did so effectively. The Israeli strikes hit their targets precisely enough to do significant damage to Hamas forces, both to its leadership and to the tunnels from Gaza to Egypt that Hamas uses to smuggle in weapons and build its growing army.(1) Doing this damage was necessary as Israel could never be safe with a strong terrorist regime in control of Gaza. As David Harris, Executive Director for the American Jewish Committee, argued: "Israel could not tolerate a terrorist regime on its border that was launching repeated rocket and mortar attacks against Israeli towns and villages."(5) Therefore there can be no debate that Israel had the right to defend itself as well as the right to determine how best to do so. While it is easy for countries and foreigners to state their opinions about Israel's security interests and how its actions may or may not fulfill them, Israel's right to make that judgment itself must be respected. Therefore Israel's military operations against Gaza were justified as legitimate self defense against Hamas and militant aggression which was putting the lives of Israeli citizens in jeopardy.