I'd like to consider the original question of why Israel joined the European Football Association from a historical {and perhaps sociological?} perspective.

Thanks to google, I found this website: http://en.wikipedia.org/wiki/FIFA

Here is an excerpt from that website:

"The Fédération Internationale de Football Association, known worldwide by its acronym FIFA, is the international governing body of Football (soccer) and the largest sporting organization in the world. Its headquarters are in Zürich, Switzerland, and its current president is Sepp Blatter...

Under the auspices of the President, FIFA [is split into six confederations which oversee the game in the different continents and regions of the world. National federations must claim membership to both FIFA and the confederation in which their nation is geographically resident for their teams to qualify for entry to FIFA's competitions (with a few geographic exceptions listed below):

    AFC - Asian Football Confederation in Asia and Australia
    CAF - Confédération Africaine de Football in Africa
    CONCACAF - Confederation of North, Central American and Caribbean Association Football in North America and Central America
    CONMEBOL - Confederación Sudamericana de Fútbol in South America
    OFC - Oceania Football Confederation in Oceania
    UEFA - Union of European Football Associations in Europe.

Nations straddling the traditional boundary between Europe and Asia have generally had their choice of confederation. As a result, nations including Russia and Turkey have chosen to become part of UEFA despite the bulk of their land area being in Asia. Israel, although lying entirely within Asia, joined UEFA in 1994, after decades of isolation by many of its Middle Eastern neighbours. Kazakhstan was the latest nation to make the move from AFC to UEFA, in 2002.

Guyana and Suriname have always been CONCACAF members despite being South American countries.

Australia have been given permission to join the AFC instead of the OFC from 2006 onwards. Australia have long lobbied for a change, because their national team is very much stronger than the other Oceania teams. No team from the OFC is offered automatic qualification to the World Cup; instead the winner of their section must play a play-off against a CONMEBOL side, a hurdle at which Australia have traditionally fallen. Perhaps ironically, Australia successfully qualified for the 2006 FIFA World Cup by winning just such a playoff in a penalty shootout against Uruguay, just a few months after the clearance to move was granted."

-snip-

So there ya go. The answer to the question "Why is Israel a member of the Union of European Football Association?" is that "although lying entirely within Asia, [Israel] joined UEFA in 1994, after decades of isolation by many of its Middle Eastern neighbours."