Then some Pharisees and teachers of the law came to Jesus from Jerusalem and asked,"Why do your disciples break the tradition of the elders? They don't wash their hands before they eat!" Jesus replied, "And why do you break the command of God for the sake of your tradition? For God said, 'Honor your father and mother' and 'Anyone who curses his father or mother must be put to death.' But you say that if a man says to his father or mother, 'Whatever help you might otherwise have received from me is a gift devoted to God, he is not to 'honor his father' with it. Thus you nullify the word of God for the sake of your tradition.
First, Jesus is against upholding traditions that contradict the commands of God. Jesus no doubt followed many customs that were not explicitly commanded by God, the use of synagogues as an example (also, modes of speech, dress, etiquette, etc). All churches, evangelical or Catholic, have traditions like this. Maybe your church always sings Silent Night during their Christmas Eve Vigil service. Maybe your church always takes the collection after music worship but before the sermon. These are just customs of practice. They are not commanded by God, but neither do they contradict the commands of God.
Second, and most importantly, the 'tradition' that is being talked about in this passage is 'the tradition of the elders'. What's being referred to here is a custom or a way of doing things, that perhaps developed over time. No one here thinks this practice came from God, it comes from 'the elders'. And this is not what Catholics mean by Tradition. In other words, the above passage isn't even referring to what Catholics call Tradition. This is what Catholics mean by Tradition:
Catholics believe that the Word of God was definitively revealed to the world in the person of Jesus Christ. The deposit of faith has been fully given and nothing will be added to it. This Word of God has been passed on in two ways:
(1) It has been passed on in writing, which we refer to as the Sacred Scriptures. It "is the speech of God as it is put down in writing under the breath of the Holy Spirit." (CCC 81)
(2) The Word of God has also been passed on "orally by the apostles who handed on, by the spoken word of their preaching, by the example they gave, by the institutions they established, what they themselves had received—whether from the lips of Christ, from his way of life and his works, or whether they had learned it at the prompting of the Holy Spirit". (CCC 76) This is called Tradition.
The teachings of both Scripture and Tradition originate only from Jesus and the Apostles. If an idea originated from a time after that, it's not a part of either the Scriptures or the Tradition. The Church may better or more fully understand or find new ways to articulate what has been passed on, but nothing can be added to either the Scriptures or to Tradition.
So Tradition does not come from man, it comes from God himself. When the Catholic Church bases something on Tradition, she is basing it on the Word of God. And since both Scripture and Tradition pass on the Word of God, they cannot contradict.
The Catechism of the Catholic Church makes a very clear distinction between what the Tradition is and what it is often misunderstood to be by evangelicals:
"The Tradition here in question comes from the apostles and hands on what they received from Jesus' teaching and example and what they learned from the Holy Spirit. The first generation of Christians did not yet have a written New Testament, and the New Testament itself demonstrates the process of living Tradition.Tradition is to be distinguished from the various theological, disciplinary, liturgical, or devotional traditions, born in the local churches over time. These are the particular forms, adapted to different places and times, in which the great Tradition is expressed. In the light of Tradition, these traditions can be retained, modified or even abandoned under the guidance of the Church's magisterium." (CCC 81)
So we have traditions, customs that have sprung up here and there for various reasons. These originate from man and can be changed or abandoned, especially if they are found to contradict the Word of God. We also have Tradition, which is a means by which the Word of God has been passed on to us. It originates in God and cannot be changed or abandoned, nor can it contradict itself or Scripture since the Word of God cannot contradict itself.
tradition isn't Tradition.