Amnesty International and other human rights organizations have decried Israel's continued aerial bombing campaign as unlawful and denounced the killing of more than 300 Palestinians since 27 December, including scores of unarmed civilians not taking part in the hostilities. Israel's attacks on the densely populated Gaza Strip also elicited condemnation from numerous world politicians and sparked protests in global cities.

Despite international outcry over escalating violence, the U.S. mainstream media continues to privilege a prepackaged narrative in which Israel's actions are never disproportionate, never counterproductive and certainly never gratuitous. According to the mainstream media, the U.S. must continue uncompromisingly supporting Israel because the allegedly beleaguered democracy is held hostage by monomaniacal Islamofascists who are inherently evil. Promoting a paradigm in which Israel is always David up against Goliath, the U.S. media presents suffering Palestinians as expendable for the greater cause of Israel winning its epic struggle. To justify U.S.'s carte blanche to Israel, the mainstream media restricts American readers to an echo chamber in which the following claims are repeated ad nausem until they are mistaken for fact:

1. Israel has a legal and moral right to bomb Gaza out of defense Security concerns are not and never have been a tolerable justification for pre-emptive attacks. Israel's decision to bomb Gaza represents a major assault on the international rule of law. The law of occupation is one of the oldest and most developed branches of international humanitarian law. An occupying power is obliged to follow the 1949 Fourth Geneva Convention, which protects the civilian population. The United Nations Security Council held in 1979 that the Fourth Convention did apply in the territories seized by Israel in 1967. Article 48 of the additional protocol is clear that Israel, as an occupying power, has obligations: "The Parties to the conflict shall at all times distinguish between the civilian population and combatants and between civilian objects and military objectives and accordingly shall direct their operations only against military objective." The latest Israeli attacks come on top of a brutal siege of the Gaza Strip which has created a humanitarian catastrophe of dire proportions for Gaza's beleaguered Palestinian residents by restricting the provision of food, fuel, medicine, electricity, and other necessities of life. "International law is not observed with respect to Israeli policies towards the Gaza Strip, Israel continues to reinforce an occupation whose every element violates international humanitarian law, and particularly the Fourth Geneva Convention," notes Jeff Halper, an Israeli-American Anthropologist, author, lecturer, political activist, and co-founder and Coordinator of the Israeli Committee Against House Demolitions.
2. Israeli citizens live in constant fear of Hamas rockets Since 2005 Hamas has fired some 6,300 rockets from Gaza at Israel, killing 10 people.[1] In just the last four days, Israel has reduced the Gaza Strip to rubble and killed over 300 Palestinians. During the ongoing four-decade-long brutal occupation of historic Palestine and the recent grotesquely inhumane blockade of Gaza, Palestinian deaths have far outnumbered Israeli deaths. Since September 29, 2000, approximately 123 Israeli children have been killed by Palestinians whereas 1,050 Palestinian children have been killed by Israelis. Since September 29, 2000, a total of 1,062 Israelis and no fewer than 4,876 Palestinians were killed in the conflict.[2]
3. Hamas refuses to recognize the right of Israel to exist and has never made any concessions As Seth Ackerman of Fairness & Accuracy in Reporting (FAIR) notes, there is no need to euphemize Hamas' history of brutal tactics or its bellicose ideology, but Hamas has signaled its potential willingness to accept a two-state settlement and make other concessions to broker peace.[3] Hamas has also made tentative offers of a long-term "hudna," or truce, albeit with less gusto than Israel demands.
4. Israel is only targeting Hamas headquarters Gaza, one of the most densely populated tracts of land in the world, is home to about 1.3m Palestinians, about 33% of whom live in United Nations-funded refugee camps.[4] Avoiding civilian casualties in the Gaza Strip during aerial raids is comparable to trying to avoid such casualties in Washington DC, New York City or Los Angeles. "Because Gaza is so densely populated, there is no such thing as precision strike – you have glass, brick, shrapnel flying into people's homes," notes Ewa Jasiewicz, a volunteer with the Free Gaza Movement.[5]
5. Attacking Hamas will help Israel achieve security There is no doubt that the recent attacks will only embolden and multiply Israel's detractors. Iran's Supreme Leader Ayatollah Ali Khamenei issued a religious decree to Muslims around the world o

I will allude to your first sentence, the rest is not of interest to me.

Self defense is never, ever illegal. Amnesty Int'l has no legal position when it comes to war or the tactics one combatant uses over another.

Israel is much more capable and more qualified than any middle eastern country to inflict greater damage on its enemy, than its enemy on it. The attacks on Israel were from the populated areas of Gaza. This is where the enemy took a stand, therefore Israel has every right to direct their air attacks where the enemy has concentrated its effort against it.

The Palestinians knew that Israel would eventually retaliate. Why then did they not move their families out of harm's way, is it because Hamas would retaliate against them if they did ?