"Crying and shooting" is the term used in Israeli political discourse to describe those Israelis who agonize over what they are doing to the Palestinians, but carry on doing it anyway. It's a way for Israelis to feel better about themselves, by reasserting their liberal, progressive and humanitarian values, even as they carry out illiberal, regressive and murderous actions.
There was a wonderful example of the phenomenon last week in a column written for Ha'aretz by Bradley Burston. He wrote an agonized column - Our Defense Forces, our war crimes, our terrorism - about the disproportionate number of civilians among the Palestinians killed by the IDF, and specifically about Israeli's collective refusal to acknowledge their responsibility for the killings.