Israel cannot apologize for what happened because that would be an admission of guilt which would open up the flood gates to law suits and it would mean saying your right we have no right to blockade Gaza and it would lead to more flotillas and petitioning the UN to declare the blockade illegal. Its not just Israeli politicians being petty. Turkey has no right to dictate if Israel can enforce a blockade of Gaza or not so Erdogan needs to either say ok I am going to end these petty demands for an apology I won't get and improve relations with Israel or say I am just going to continue to downgrade ties. Its going to cost Turkey money through lost tourism and they can't buy advanced Israeli weapons. Israel in the meantime has improved its relations and upgrading military cooperation with Turkeys enemies Greece & Cyprus. Israel also has good relations with the Kurds and supports the creation of a Kurdish state. Israel has made more friends from the breakdown of relations with Turkey and now Turkey is about to lose its main arab ally ( Assad ). Go for your plan B Erdogan it won't get you an apology and it won't lead to an end to the blockade of Gaza.
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from the article: Turkey President: Expulsion of Israeli envoy is just the first step