Why catechumens would spit symbolically on Satan before being baptized

Those to be baptized in the early Church renounced Satan by facing West and spitting on the ground.

The current rite of Baptism states that those to be baptized, or the sponsors in their place, should make an act of renunciation of Satan.

Do you reject Satan?
I do
And all his works?
I do.

In the early Church, this act of renunciation was much more prominent and included several physical acts.

According to the Catholic Encyclopedia, this included facing West and spitting at Satan.

The catechumen, standing with his face to the West, which symbolized the abode of darkness, and stretching out his hand, or sometimes spitting out in defiance and abhorrence of the devil, was wont to make this abjuration.

Sometimes this would include spitting on particular idols that the catechumen formerly worshiped.

St. Cyril of Jerusalem adds a few more details of this ceremony before baptism.

First ye entered into the vestibule of the Baptistery, and there facing towards the West ye listened to the command to stretch forth your hand, and as in the presence of Satan ye renounced him.
[Y]ou are bidden to say, with arm outstretched towards him as though he were present, I renounce you, Satan. I wish also to say wherefore ye stand facing to the West; for it is necessary. Since the West is the region of sensible darkness, and he being darkness has his dominion also in darkness, therefore, looking with a symbolic meaning towards the West, you renounce that dark and gloomy potentate.

This is an important aspect of Baptism, as it severs any tie one might have to Satan, pledging instead to worship Jesus and be at his service.

St. Cyril explains that the catechumen would then turn to the East, accepting the light of Christ.

When therefore you renounce Satan, utterly breaking all your covenant with him, that ancient league with hell, there is opened to you the paradise of God, which He planted towards the East, whence for his transgression our first father was banished; and a symbol of this was your turning from West to East, the place of light. Then you were told to say, I believe in the Father, and in the Son, and in the Holy Spirit, and in one Baptism of repentance. Of which things we spoke to you at length in the former Lectures, as God’s grace allowed us.

While the current rite of Baptism isn’t as physical in the act of renunciation, it still remains a powerful ceremony, one that is repeated every Easter Vigil, when everyone present professes the words of renunciation anew.