Unlike in the US, where the President nominates members to fill judicial openings and the Senate confirms, in Israel the appointments are made by a majority of the judicial selection committee. The Committee has nine members: three judges, two members of Israel's bar association, two members of the government, and two members of the Knesset. Historically, the judges have been able to veto choices even if they were in the minority.
In the case of Gavison, the three judges plus MK Avraham Shochat (Labor) and a member of the Bar oppose her confirmation. That's a majority and will make it very unlikely that she'll sit on the Court.
The opposition stems from her statements about the role of the court in a democracy (i.e., separation of powers). She has crazy fanatic beliefs like the courts shouldn't dictate policy over the will of the majority. Since, as Robert Bork once said, Israel's SC is the most activist court in the world, Barak does not want judges who oppose that ideology.
"Since the creation of the Supreme Court, we have never asked candidates for their opinion on the role of court. These are things that a judge learns, internalizes and defines in the process."
That's retarded. Judges are not supposed to understand their role before they get on the Court? What does that mean? That's like saying pitchers aren't supposed to understand the rules before they start playing the game. If rules exist in the legal world, and some of those rules deal with the boundaries of the court's power, then a judge must have a position on what those rules are before she sits on the court. How can she decide a case that involves striking down a legislative act without understanding what her job is supposed to be?
This whole opposition is a pretext. And the scary thing is the farce is not designed to keep a right-winger off the court; Gavison is no such thing. They refuse to confirm her because she wants to limit the court's power so it cannot protect democracy from itself.