When asked whether the scapegoat could be carried if it became sick, Rabbi Eliezer answered “that goat can carry me and you.”
When asked whether a replacement for the person who escorted the scapegoat to the cliff could be inserted if the first person became ill, he answered “I and you shall be in peace.”
When asked whether the person who escorts the scapegoat should go down and kill it in the event that it did not die in the fall off the cliff, he answered by quoting a passage in Sefer Shoftim (5:31) “So may all your enemies perish, Lord.”
Perhaps the simplest way of understanding Rabbi Eliezer’s answers is that he was suggesting that these situations would never occur, and therefore there was no need to discuss them in a serious way.
Many of the commentaries argue that Rabbi Eliezer was not avoiding the questions, rather he chose to express his opinion on them in an indirect manner. His answer that the scapegoat could carry the people hinted that such carrying would be permissible on Shabbat. Saying that they should remain in peace indicated that anyone could step in and be a fitting substitute for the designated person who became ill. Finally, quoting the passage in Sefer Shoftim showed that he felt that once the commandment was fulfilled and the scapegoat was thrown from the cliff, no further involvement was necessary. In fact, the Jerusalem Talmud reports that the scapegoat occasionally escaped into the desert.
The Gemara recounts several other questions that were presented to Rabbi Eliezer, about which he gives unclear responses, and explains that he was not simply trying to avoid the questions, rather he was abiding by his personal position of never offering a ruling that he did not have a tradition on from his teachers (see Sukka 27b, where Rabbi Eliezer explains this position). Nevertheless it should be noted that this holds true only for questions of a final legal ruling. With regard to the arguments and discussions that took place in the bet midrash , he certainly played an active role that included his own original suggestions.