I don't really see where Avineri does that, he doesn't discuss opposition to Zionism at all since that is not the subject of the piece. However he acknowledges that only a small minority of Jews who left Europe during the period in question went to Palestine, and that Jews responded in different ways to the various problems they faced in reconciling their identity with the demands of modern European nationalism. It's just a short piece clarifying how Zionism was in its origins a secular response to the challenges facing late nineteenth century European Jews (which is the only reason I posted it), but it doesn't state or imply that Zionism was the only secular response. A broader discussion on that topic would eat up a lot more than twelves pages, but for what it's worth, Avineri has written the following in a different piece:
"the end of the 19th century witnessed the birth not only of Zionism but of a number of different attempts to “normalize” the status of Jews. In the annus mirabilis of 1897 Herzl convened the First Zionist Congress in Basel in August, the Jewish socialist Bund was founded in Vilna in October, and the leading industrialist Walther Rathenau published a haunting and somewhat neglected plea for radical assimilation, evocatively titled Hear, O Israel, in Berlin. Political Zionism argued that normalization could be achieved only if the Jews were to have a state of their own, like all other nations; the Bundists argued that Jews should strive for integration into the societies in which they were living through a universal socialist revolution that would nonetheless give them a distinct place in the new world order alongside other nations; and Rathenau suggested that Jews could attain integration into German society if they would redefine themselves as a German tribe, like Saxons, Bavarians, or Prussians...
... Despite its efforts to reach out to the Jewish masses and to win over world public opinion, the Zionist organization established in Basel remained a very modest enterprise until World War I. It continued to hold annual congresses even after the early death of Herzl in 1904. It helped to inspire Jewish immigration to Palestine and the founding of a number of villages and towns, including Tel Aviv, but it remained marginal in Jewish life and world politics. The Bund, on the other hand, despite its small start in a Vilna basement, became a mass movement, at one time numbering more members than the general Russian Social Democratic Labor Party, with which it was affiliated. For a time after World War I, it was the largest Jewish party in the Sejm of independent Poland. Rathenau’s call for radical assimilation did not ameliorate the position of German Jews. Rathenau himself, who helped more than anyone else to organize the German economic war effort and later became foreign minister in the Weimar Republic, was assassinated in 1922 by an ultranationalist, anti-Semitic German militia that accused him of treachery."
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