Israelis are mixed, some came from Europe, some from USA, Africa, Arab countries, etc. These immigrants brought with them their own cuisines. Arabs on the other hands (middle east Arabs) largely used Turkish cuisine. But in the case of falafel, it is with no doubt Arabic food. Some variations of it exist, but the falafel that is served in the middle east is the Arabic version, and believed to be the original version of it. As for other things, if you look into the Israeli communities, most of their Music is Arabic style, or Greek sometimes. They hold Belly Dance competition, Arabic Classic Music Competitions, and etc. And that is not bad, they Live in the Middle East and they inherited parts of the traditions. The point is that Falafel, Arabic Music, Cuisine in general, Belly Dancing, Arabic Classic Music (Playing Aud, and Kanoon), Shawerma (Turkish)m Shaish Tawook (Turkish), Kebab (Turkish), Baklava, Knafa, etc is all middle eastern cuisine, and Israel is Part of the middle east. But never they should claim any of these is their tradition, and own food, music, culture.
First refugees travelling on Hungarian bus arrive at Austrian border (Reuters)
from the article: No matter where it originated, falafel is still Israel's national food