It is effective because it makes listeners feel unified is the best reason why president Wilson uses the word "we."
In his speech, "War Message to Congress", President Woodrow Wilson uses the word "we" as it is their way to include the American People in their message to the Congress, thus playing a double role in his speech, on the one hand as a pious and genuine representative of the people, and on the other, as a member of the party.
The word "we", included in a speech which was given by a leader, tends to include in the message the members of the group over which the leader exerts influence. As in this scenario, Wilson speaks for the people, saying that it has no problem with the German people.
Hence, the correct answer is - it is effective because it makes listeners feel unified.
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