Why does it say "v'Einam"?
Rav Sadya Gaon: Our fathers were destroyed.
Ri Kara: They already died.
Palgei Mayim: Hashem did not consider our fathers' sins against them.
Are we punished for our fathers' sins?
Rav Sadya Gaon: Yes, also we are punished for them.
Ibn Ezra: Our sins join with theirs. They escaped and we did not. This is like "Poked Avon Avos Al Banim" (Shemos 20:5).
Ri Kara: We were exiled from our land and the Bayis was destroyed, not only due to our sins. Rather, the sin of all generations was put on our generation. Chazal said 'Tzidkiyah drank the dregs of all generations' (Seder Olam Rabah 28).
Palgei Mayim: The Ari Zal wrote that the son's Nefesh is latent in the father's Nefesh. Sometimes, if the son will be a Rasha, it causes the father to sin. Therefore, we confess and say that due to our many sins, all our fathers' sins are considered ours, for we caused them 1 . This is why "Poked Avon Avos Al Banim."
Surely the father had free choice! Some great Tzadikim had children who were Resha'im, e.g. Yitzchak fathered Esav! Perhaps this requires great Avodah; when the father did not overcome the 'influence' of the son, the sin is attributed to the son. Even Avraham weakened in Dan (Bereishis 14:14), for later his descendants would sin there (Sanhedrin 96a). (PF)