"Why did Jesus have to be a human?" Has anyone ever asked you a tough question like that? How did you respond? Both Not-Yet-Christians exploring the faith and baby Christians learning the faith ask questions like this. Even our own children ask penetrating questions about the nature of Jesus and the gospel we confess.
Sometimes, we avoid talking about our faith because we don't have the words to describe it. Even if we affirm Jesus was both God and man—both divine and human—we still struggle to answer some of the "why" questions like the one above. We think to ourselves: "I've got to study that more" or "I'll have to ask the pastor about that one" (which really leaves you in deep water when you ARE the pastor!). But so often we never do and we miss a prime gospel opportunity for evangelism or discipleship.
This brings us to the second benefit of Catechisms: Catechisms promote evangelism and discipleship by summarizing the promises and commands of scripture concisely and memorably.
Take the question above for example. Say you were explaining Jesus to a Not-Yet-Christian. You read John 1:14: "And the Word became flesh and dwelt among us...."and then you try to explain that the Word is Jesus and Jesus became flesh (i.e. human) in the incarnation (what we celebrate at Christmas). "Why" is a perfectly natural question. Imagine if you had this in your pocket as an answer: Jesus became truly human so that "in human nature he might on our behalf perfectly obey the whole law and suffer the punishment for human sin; and also that he might sympathize with our weaknesses." (New City Catechism Question 22.)
Sure, it would take some explaining to help a Not-Yet-Christian understand what you are saying. But the key is, it would give you a solid starting point. Having such jumping-off points in the back pocket of our brain increases our confidence to engage those who don't know Christ with the precious truths of the gospel. Just think about all the good discussion you could have with someone who doesn't know Jesus about Jesus' ability to "sympathize with our weaknesses". You get the point.
The same benefits apply for discipleship. For parents longing to disciple their children in the gospel, the catechism provides a firm foundation of truth. Will children understand everything in the catechism? No. But it will give them language to answer life's questions from a gospel perspective. When they're faced with questions like "Where did all this come from?" instead of only hearing the answers of a god-less naturalistic worldview (it all came from a big bang followed by billions of years of evolution), they will hear in their head and say with their mouths: "God is the creator and sustainer of everyone and everything....He created all things by his powerful Word, and all his creation was very good; everything flourished under his loving rule." (New City Catechism Questions 2 & 5).
As children grow and as Not-Yet-Christians become baby Christians, Catechisms provide starting points (a syllabus if you will) for deeper study of truth. They begin from the truth ("God is the creator and sustainer of everyone and everything.") and ask "Where is that in the Bible?". And so begins a lifetime of diving into the rich truths of scripture and feasting on the Words of life. Catechisms done well should lead to a lifetime of love for the basis of the catechism—the Word of God.