According to Catholicism, why did the robbers strip the traveler to Jericho?
First of all, it must be stated that this story as recount by Our Lord is indeed a parable.
The parable of the Good Samaritan is a parable told by Jesus in the Gospel of Luke. It is about a traveller who is stripped of clothing, beaten, and left half dead alongside the road. First a priest and then a Levite comes by, but both avoid the man. Finally, a Samaritan happens upon the traveller. Samaritans and Jews despised each other, but the Samaritan helps the injured man. Jesus is described as telling the parable in response to the question from a lawyer, "And who is my neighbour?". In response, Jesus tells the parable, the conclusion of which is that the neighbour figure in the parable is the man who shows mercy to the injured man—that is, the Samaritan.
Some Christians, such as Augustine, have interpreted the parable allegorically, with the Samaritan representing Jesus Christ, who saves the sinful soul. Others, however, discount this allegory as unrelated to the parable's original meaning and see the parable as exemplifying the ethics of Jesus.
Origen described the allegory as follows:
The man who was going down is Adam. Jerusalem is paradise, and Jericho is the world. The robbers are hostile powers. The priest is the Law, the Levite is the prophets, and the Samaritan is Christ. The wounds are disobedience, the beast is the Lord's body, the [inn], which accepts all who wish to enter, is the Church. ... The manager of the [inn] is the head of the Church, to whom its care has been entrusted. And the fact that the Samaritan promises he will return represents the Savior's second coming.
John Welch further states:
This allegorical reading was taught not only by ancient followers of Jesus, but it was virtually universal throughout early Christianity, being advocated by Irenaeus, Clement, and Origen, and in the fourth and fifth centuries by Chrysostom in Constantinople, Ambrose in Milan, and Augustine in North Africa. This interpretation is found most completely in two other medieval stained-glass windows, in the French cathedrals at Bourges and Sens." - [Parable of the Good Samaritan](Parable of the Good Samaritan)
The Catholic Encyclopedia puts it this way:
The good samaritan is certainly authentic; it can be explained mystically in detail, and is therefore as much an "allegory" as a parable. If it was spoken by our Lord so was the wicked husbandmen. It does not exactly reply to the question "Who is thy neighbour?" but propounds and answers a larger one, "Whom in distress should I like to be neighbour to me?" and gives an everlasting instance of the golden rule. At the same time it breaks down the fences of legalism, triumphs over national hatreds, and lifts the despised Samaritan to a place of honour. In the deeper sense we discern that Christ is the Good Samaritan, human nature the man fallen among robbers, i.e., under Satan's yoke; neither law nor Prophets can help; and the Saviour alone bears the charge of healing our spiritual wounds. The inn is Christ's Church; the oil and wine are His sacraments. He will come again and will make all good. The Fathers, Sts. Ambrose, Augustine, Jerome, are agreed in this general interpretation. Mere philanthropy will not satisfy the Gospel idea; we must add, "the charity of Christ presseth us" (2 Corinthians 5:14). - The good Samaritan (Luke 10:37)
While in the seminary, we were told that it the reasons why the robbers in Our Lord’s days would have stripped pilgrims or travellers of their cloths would have been two fold:
If the robbers believed, the victim to be dead, he had no need of any clothing and thus was despoiled of all that he was carrying at the moment. Clothing, we must remember was a commodity that was treasured by both thieves and executioners. The Passion of Christ bears this out when the soldiers drew lots for Christ’s tunic.
A second element to be added to this scenario is that if the victim was not dead, he would have been unable to look for his assailants because he was naked and now needed clothes to continue his journey.
Thus these robbers were truly doing what was in their best interests when they left him half dead.
The Good Samaritan by Jacob Jordaens