Hannah Arendt explains this in her account of the Eichmann trials in Eichmann in Jerusalem.

Basically, many believed that simply sentencing Eichmann to death was "unimaginative" and allowed him a quick and easy escape from true punishment. To give him the death sentence in the manner they did (2 hours after his plea was rejected) was not seen as punishment enough. Some suggested that Eichmann should have spent the rest of his life doing hard labor in Israel as a sort of poetic justice, forcing him to die the way he enabled millions of Jews to die. One more extreme idea is the suggestion that Eichmann should have been shackled in the streets and have a public ceremony held to shame him and idolise those who tried him in court.

Beyond that, Arendt suggested the trial itself was a faulty and rigged, ignoring facts of Eichmann's lack of involvement in Eastern Europe, where most of the genocide occurred. Not at all saying he was exempt from blame, but that the Israeli court essentially blamed Eichmann for the entire Holocaust and claimed he was its leading authority, which was not exactly true.

Martin Buber specifically argued that just hanging Eichmann (which is actually what Eichmann himself wanted) exonerated all German youth from feeling guilty about the Holocaust. This argument was really just to encourage Holocaust rememberance and to not make the crimes feel like a relic of the past. By killing all perpetrators of the Holocaust, Germany might feel as if the Holocaust was behind them and they no longer should carry the guilt and burden.

TLDR: Death was too east an escape from what otherwise could have been a lifetime of torture. Some felt he deserved worse punishment, and some believed that by killing Eichmann, Germany would forget and exonerate itself from guilt over the Holocaust.

(edited to add more.)