It's culturally closer to Europe than to its Muslim neighbors. Israel competes in the Eurovision song contest and in the European soccer confederation.
Yes, because of the long-standing occupation of the Palestinian territories, the lack of rights afforded to the Palestinian Arabs living there and the ever growing Israeli settlements in and around these Palestinian communities, Israel isn't very welcomed by its other Arab nations.
Except when it comes to its apartheid-like policies in the West Bank, but then again formally Apartheid South Africa was long accepted as part of the West too...
Why Morocco considered East, while Greece West?
Geographically Morocco is 2500km to the west from Greece, culturally Morocco is predominantly Muslim, while Greece Christian.
Also geographically almost whole Republic of Azerbaijan, parts of Russia, Turkey and Kazakhstan are considered in Europe.
The Kazakhstan case is funny, considering it's bordering China.