Should one move to Israel?
The Gemara relates that there was a disagreement among the Sages of the Gemara regarding this question.
Rabbi Abba was avoiding being seen by his teacher Rav Yehuda, as Rabbi Abba sought to ascend to and his teacher disapproved, as Rav Yehuda said: Anyone who ascends from Babylonia to transgresses a positive commandment, as it is stated: “They shall be taken to Babylonia and there they shall remain until the day that I recall them, said the Lord” (Yirmiyahu 27:22). Rabbi Abba did not want to discuss his desire to emigrate with Rav Yehuda. Nevertheless he said: I will go and hear something from him at the hall where the Sages assemble, without being seen, and afterwards I will leave Babylonia.
The Gemara in Massekhet Ketubot (daf 110b) relates a similar incident regarding Rabbi Zeira who, like Rabbi Abba, was a student of Rav Yehuda who desired to move to Israel. According to that Gemara, the proof-text brought by Rav Yehuda from Sefer Yirmiyahu was understood by Rabbi Zeira as referring specifically to the Temple vessels that had been looted by the Babylonian troops. According to his approach, those vessels would not be returned until the time of redemption, but the passage does not relate at all to moving to Israel.
Tosafot point out that in any case, the context of the passage in Yirmiyahu clearly relates to the period following the destruction of the first Temple; nevertheless Rav Yehuda chose to apply it to his time, as well. Apparently even according to Rav Yehuda’s understanding, the prohibition – which is unique to Babylonia – did not apply while the Temple was standing, for then there is clearly a mitzva to immigrate to the land of Israel and fulfill the mitzvot that are connected with the land of Israel. However, Rav Yehuda maintained that after the destruction of the Temple it was forbidden to leave Babylonia.