Israel and Turkey are indeed natural allies. They dont have any disputes. We have common enemies and opponents. Syria used PKK against Turkey exactly as it used PLO, Hezbollah and Hamas against Israel. Armenian terror group ASALA in Lebanon carried joint excercises in Lebanon with PLO and PKK. ASALA was destroyed by Israel together with PLO. Iran helped Armenia against Azerbaijan. Azeris dont forget it and maintain good relationships with Israel even today. Greeks were traditionaly very pro Palestinian.
Erdogan however decided to return Turkey to pan-Islamism. The easiest way to increase popularity among the Arabs is curse Israel. So he started his trolling. The reason why Israel did not apologice is that it became clear that nothing will change. Erdogan will keep cursing and attacking Israel, military ties wont restore (Erdogan destroyed military cooperation before flotilla). Erdogan is in trouble: his idea of union with Syria and Iran miserably failed, Palmer report was in favor of Israel, trade deficit is rapidly growing. So he hardened his rethorics against Israel even more to divert attention these failures. But what he can actually do? - Nothing much. He already used all his cards.