What do you mean by "giving them some air to breath"?
Israel is making the Palestinians' life as good as possible. Supplys medications, food, electricity, water and all sorts of humane aid on a daily basis to the people of Gaza, even now. The IDF does the best to kill as few civilians as possible, warns them few minutes before bombing the house. If they would just cooperate and fucking leave the damn house (Hamas' arsenal) , there would barely be any innocent casualties. But, of course, they choose to listen to Hamas and stay, sacrificing their and their families life for the "grater good", so that the entire world will see the IDF and the Israeli leadership as cruel and inhumane.
Of course, they are idiots like in those that video that just want to take all the arabs and throw them into the sea. But the world press make all of you believe that is the general opinion of the Jewish community, when it's simply not the case. Hamas' lies and public relations services are better the the Israeli Public diplomacy, that is all.