(For more info about Eden Abergil, see article below: "O Abergil...".)
#5: Abergil's political views are so far right that she makes him look like Kadima by comparison -- maybe next election he can broker a deal with them.
#4: Someone has actually heard of her.
#3: Appointing her to any position would be such a blunder that it would take the spotlight off the corruption charges against Lieberman currently under investigation.
#2: Abergil is the only known Israeli to be even more tactless than Deputy Foreign Minister Danny Ayalon. If that doesn't sound like diplomat material I don't know what does.
#1: She's the only right-wing Israeli who can manage a sit-down, let alone a photo-op, with Palestinians.
Any other suggestions?