“Remember what Amalek did to you, on the way, when you left Egypt. Who happened upon you, on the way. . .” (Devarim 25:17-18)

Why are the words “on the way” (baderech) repeated? And why is the first “you” in the singular (lecha), while the second is in the plural (b’tzeitchem)?

It seems to me that while the first “on the way” refers to Israel (“when you left Egypt”), the second refers to Amalek.
They were a nomadic tribe of brigands who traveled around looking for pillage and loot, and they happened upon Israel, whose rear guard (kol hanechshalim acharecha) offered an easy target (25: 18). Far from seeking out Israel in particular, they were constantly on the move (“on the way”) seeking objects to attack. Their only justification was the need to plunder to make a living.

This explains the eternal enmity decreed between G-d and Amalek (Shemot 17: 16). If Amalek were motivated by ideology or religion to attack Israel, then that ideology or that religion could, in the time to come, be channeled into true avodat haShem, as would be the case with all the other nations. But for a society lacking any ideology beyond preying on its neighbors, there is no hope.

Why does the Torah use the singular in referring to the effects of Amalek’s attack on Israel? Because it not only affected the Israelites who left Egypt, it impacts on each of us today.

This is what my son wrote while serving in the IDF:
“What Amalek did, it did to you, as an individual… What did it do? It acquainted us with war and with the culture of war. That we have a worldview in which war exists, can be legitimate, and sometimes we sanctify it—that is what Amalek did to us. This is what we are commanded to blot out from under the heavens: war, the culture of war, and violence in particular and in general: to both remember Amalek and to blot out its residue or effects (zecher), and not to make war part of our worldview.

”…But since there is war in the world, complete pacifism is a fatal mistake, for if a man does not protect himself there will come someone who is not a pacifist and destroy him. For that reason, “when haShem gives you respite from all your enemies around you” (Devarim 25: 19)—only then, when there will no longer be a need for war to preserve our existence, will come the time to blot out the culture of war and its influence—the zecher of Amalek—from under the heavens.”