William Burkitt on Matthew 21:4

Here the reason is assigned why Christ rode upon the ass into Jerusalem; it was to fulfil an ancient prophecy, that the Messiah, or King of the Jews, should come riding upon that beast into Jerusalem. There was not any prophecy of Christ more plainly fulfilled than this. The prophecy alluded to, is Rejoice greatly, O daughter of Zion; shout, O daughter of Jerusalem: behold, thy King cometh unto thee; he is just, and having salvation; lowly, and riding upon an ass; and upon a colt the foal of an ass. Zeph 3:20

Where note, The character given of the Messiah; he is the Supreme King and Governor of his church, thy King cometh. The errand that he comes upon, bringing salvation; and the entertainment which his church was to give him; namely, to receive him with triumphs of joy, and universal acclamations. Rejoice, O daughter of Zion; and shout, O Jerusalem, for joy.