The reason the EUMC definition is discredited is simple: It confuses the state of Israel with the movement known as Zionism, and seeks to label anybody who criticises either as an anti-Semite when it is perfectly possible to do so without wishing harm on Jewish people.
Zionism is the belief that Jews, just like any other people, are entitled to a state of their own and that that state is called Israel. To be opposed to Zionism is the same thing as being opposed to the existence of Israel.
These, for the sake of handy reference, are the parts which, in the eyes of the OP, render the EUMC definition "discredited":
Contemporary examples of antisemitism in public life, the media, schools, the workplace, and in the religious sphere could, taking into account the overall context, include, but are not limited to:
[...]
Accusing the Jews as a people, or Israel as a state, of inventing or exaggerating the Holocaust.
Accusing Jewish citizens of being more loyal to Israel, or to the alleged priorities of Jews worldwide, than to the interests of their own nations.
Examples of the ways in which antisemitism manifests itself with regard to the State of Israel taking into account the overall context could include:
Denying the Jewish people their right to self-determination, e.g., by claiming that the existence of a State of Israel is a racist endeavor.
Applying double standards by requiring of it a behavior not expected or demanded of any other democratic nation.
Using the symbols and images associated with classic antisemitism (e.g., claims of Jews killing Jesus or blood libel) to characterize Israel or Israelis.
Drawing comparisons of contemporary Israeli policy to that of the Nazis.
Holding Jews collectively responsible for actions of the state of Israel.
The very next sentence in the definition runs:
However, criticism of Israel similar to that leveled against any other country cannot be regarded as antisemitic.
But Mr Sivier is not interested in that sort of criticism; he wants to demonise Israel, deprive it and its population of any right commonly enjoyed by citizens of other countries while attacking Jews outside Israel for having any feelings about a country where 40% of the world's Jews live, and where many have family, other than wishing for its obliteration. As it is, about 90% of Jews outside Israel believe Israel should exist; that is, not least, because Jews have needed somewhere where they know they will be taken in, having been expelled from country after country since 1948 as well as before. So Mr Sivier is not antisemitic; he just feels that nearly all Jews are fair game for attack in whatever way he deems fit.
It seems clear that “Jewish Labour Movement” is a misnomer. It should be “Zionist Labour Movement”.
Had this been Poland in the 1920s, Mr Sivier might have had a point. But we're talking about the UK, where Jewish socialists in the Labour Party have been overwhelmingly Zionist for nearly a century. It also happened that the main opposition to the Zionists in Poland, the Bundists, were virtually all exterminated in WW2. This, it shouldn't have to be said, was persuasive to the few surviving Jews of the virtues of the Zionist case.
Change that single word and the motivation behind the suspension of Ms Walker becomes clear.
Except that the things she said that were so offensive were to claim that Holocaust Memorial Day did not commemorate other genocides, which it does (including the genocides in Bosnia and Rwanda, regularly denied by many ideological bedfellows of Mr Sivier and Ms Walker), and that, despite the attacks on Jewish elementary schools in Europe, Jewish elementary schools in the UK should have no more security than any other elementary school (at a time when antisemitic hate crime is spiraling). It takes considerable prowess in mental gymnastics to associate commemorating genocide and ensuring the safety of Jewish elementary schoolchildren in Britain with Israel. If someone's conflating the issues here, it doesn't look like it's the JLM.
The Jewish Labour Movement does not represent Jews who are not Zionists. It persecutes them.
The evidence for the persecution of anyone by the JLM is about the same as the evidence for the persecution of Southern Baptist pastors by same-sex couples intent on marriage, i.e. nonexistent. It's not as if membership in the JLM is compulsory, or that Jewish members of Labour unhappy with it cannot set up their own group. Indeed, there is a vocal group of non-Zionist Jews called Jewish Socialists; while it only has about twenty members whose attachment to their Jewish heritage seems mainly to consist of signing letters to the press attacking all things Israeli, and while many of these twenty are not in the Labour Party but in parties to its left, that does not prevent its voice being widely heard in the party and well-received by people such as Mr Sivier. For a "persecuted" group, they seem to be very popular and effective.
Jackie Walker, although Jewish, is not a Zionist.
Her "Jewishness" is through a father she never met. She was not raised Jewish, nor has she at any stage identified with the Jewish community. However, since engaging on her career of Jew-baiting, the fact of her Jewish descent has become important to her. She also believes that, despite the lack of any evidence, Jews were the "main funders" of the slave trade. Make of that what you will.
This is not about anti-Semitism; it is about removing a person who does not support Zionism from a position of influence.
Here is an account of why the decision was taken by someone on the committee that took it. That person is in a party to the left of Labour. It is impossible to draw the conclusion Mr Sivier does from her account.