Rabbi Chaim of Brisk separated from “Agudas Yisroel” after the Katowice conference.
His reasoning is described in “Mikatowitz Ad Hei B’Iyar“, p. 56 (find more background over here):
Rabbi Chaim Soloveitchik of Brisk was invited by the German architects of Agudath Israel to their founding conferences in 1909 and 1912, but afterwards he withdrew his support from it. Family members relate that Rabbi Chaim gave the following analogy to explain his opposition to the Moetzes Gedolei Hatorah: In the old times, everyone had a candle in his house to give light. It was a small candle, but a candle nonetheless. And even if someone did not have a candle in his house, there was always a candle in his neighborhood that he could use. But then they built an electric power station to supply light to the entire city at once. Once the electricity was running, nobody kept candles in his house anymore, and if, G-d forbid, the power station stopped working, the entire city would be in the dark, with no source of light.
Rabbi Chaim in his wisdom foresaw that a worldwide Orthodox organization could be a good thing, but could also be a very bad thing. As long as every rabbi is independent, even if some rabbis err, there will always be some still on the right path. But when all rabbis subscribe to a single organization, if something goes wrong with that organization, all of its members go down with it. With eerie accuracy, Rabbi Chaim’s analogy foreshadowed events that took place many years after his passing, when the Agudah activists in 1947-49 led their followers into full-fledged participation in the Zionist enterprise, without the benefit of any ruling even from their own rabbinical council.
(I doubt the last, editorializing sentence is factual.)
And his point is that “if something goes wrong” is not an “if”, but rather a “when”! (Not to mention related arguments.)
The electric power plant metaphor was also used by the Chafetz Chaim to great effect, see what we once wrote here.
But this serves as an argument against any organization not mandated by the Torah (Beis Hamikdash, courts) such as the state! Indeed, Rabbi Chaim Brisker was “anarchic”, not just in his “lifestyle”, but also in his politics, as opposed to Rabbi Yoel Teitelbaum, who was fine with any Goyish state except Israel (endorsing democratic government in Vayoel Moshe!) and furthermore would be completely on board with the same kind of super-oppressive totalitarianism (beyond limited statism, which, itself, inevitably prevents Jews keeping mitzvos from free will), as long as it was under Mashiach’s management…
His son, Rabbi Yitzchak Ze’ev was similar. This is how I interpret the Satmar Rebbe’s following testimony.
“Tiferes Yoel” (part four, chapter 145), as quoted elsewhere:
But what can this mean? One logically cannot be more extreme than the rabbi who called the State of Israel satanic and all involved parties worse than idolaters. So, I suspect he means as I said.