The Chofetz Chaim opposed Zionism because it violates the principles of Yaakov Avinu and our code of conduct in exile.
He wrote: “The Torah teaches us not to resist the nations even when they fight against us. We must follow in the footsteps of Yaakov Avinu in his encounter with his brother Esav. As the Ramban writes in Vayishlach, all that happened between Yaakov and Esav happens to us constantly with Esav’s children. We must adopt the methods of that tzaddik, to make the three preparations that he made: prayer, a gift, and escape through war, that is, to flee and take refuge. As long as we walked on that well-tread path, Hakadosh Baruch Hu saved us from their hands. But since we have strayed from the path and new leaders have arisen who chose new methods, leaving behind our ancestors’ weapons and adopting the methods of our enemies, we have fared worse and worse, and great travails have befallen us. May Hashem have mercy on our people and restore our judges as of old." (Chofetz Chaim Al Hatorah, Devarim)
And in another place he writes: "If the activists of our time were wise, they would understand that they must not provoke the nations or fight wars against them. Rather they must first study the parsha of Yaakov's meeting with Esav, the Parsha of Golus, and then follow in the footsteps of our wise ancestor. Then they would succeed in improving the lot of the sheep among the seventy wolves." (Chofetz Chaim Al Hatorah, Shmini)
Rabbi Yaakov Kamenetsky said that it was in reaction to Zionism that the Chofetz Chaim, in the 1890s, began to stress the study of Kodashim. (He wrote Likutei Halachos, started a Kodashim kollel, and taught Eizehu Mekoman to the unlearned kohanim in Radin.) That was the period of the first Zionist aliyah, and the Chofetz Chaim saw their goal, to establish an independent Jewish colony in Eretz Yisroel, as an implicit denial of the coming of moshiach and the complete redemption to be brought by Hashem. Therefore he taught the Jewish people to make a point of studying the laws of the service in the Beis Hamikdash, in order to reinforce the belief in moshiach. (Bimechitzas Rabbeinu, p. 31)
The Chofetz Chaim gave a parable to encourage the Jewish people in their long wait for redemption: “One day, the army received an announcement that the king himself would come that very day to visit the army camp. All the soldiers lined up in rows, weapons in hand, waiting for the king to come. The general and his officers stood at the front. They waited several hours, but the king did not arrive. Eventually, the general grew tired of standing, and he asked someone to bring him a chair. He sat down and dozed off in the chair.
Suddenly at that moment, the king and his entourage arrived, and all the soldiers saluted him. The sleeping general, too, awoke and wanted to stand up in honor of the king, but the king told him to remain seated, and gave orders that he be demoted from his position.
“If you couldn’t stay standing for just a few more minutes together with the rest of the army, then you are not a faithful soldier,” said the king. “All the simple soldiers, who get a low salary, were able to wait, but you, with a salary many times higher, could not.”
“And so it is with us,” the Chofetz Chaim concluded. We all say in our prayers, “We are waiting for You.” We wait for moshiach tzidkeinu. But in one moment we grow tired of waiting and want to sit down on a chair. We have to be patient so that we do not lose everything in a few minutes, like that general did.” (Printed in “A Hundred Stories and Parables of the Chofetz Chaim” by Rabbi Shmuel Greineman, number 19)