According to Scripture, is the Catholic Church infallible?

Let's see if you can follow my logic.

Scripture says that the Church teaches the Wisdom of God:

Ephesians 3:10
To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God,

Is God's Wisdom infallible? I say yes.

Is there really any need to say more? I don't think so. But there is more.

Scripture says that the Church is the pillar and ground of the truth:

1 Timothy 3:15
But if I tarry long, that thou mayest know how thou oughtest to behave thyself in the house of God, which is the church of the living God, the pillar and ground of the truth.

God is here saying that the Church always upholds the truth. I believe God. Therefore, I conclude that the Church is infallible.

Scripture says:
Matthew 16:18
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.

Here the Church is depicted as keeping hell in a state of seige. And further it is said that hell will never prevail against the Church. If the Church committed errors in the mission given her by God, then the gates of hell would have prevailed. God says that won't happen. I believe God. Therefore, I conclude that the Church is infallible.

But is this the Catholic Church?

I believe the Church described in Scripture is the Catholic Church, yes.

First, Jesus Christ appointed a Pastor as head of the entire Church:
John 21:17
He saith unto him the third time, Simon, son of Jonas, lovest thou me? Peter was grieved because he said unto him the third time, Lovest thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I love thee. Jesus saith unto him, Feed my sheep.

I see only a few Churches with such a Pastor. Further, Jesus Christ said that the Pastor over His Church would be infallible:

Matthew 16:17-19 (King James Version)
17And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.18And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. 19And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.

The list of Churches accept this teaching gets smaller. Certainly, all Protestant denominations can now be eliminated.

Jesus Christ not only said that the Pastor was infallible but Scripture describes the Church as infallible:

Ephesians 3:10
To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God,

The list remains the same, but now I can certainly eliminate all Protestant denominations.

Back to Matt 16:18, Scripture says that Jesus Christ established one Church. History shows that all the Churches sprang from the Church which is frequently described as the Mother Church. The Catholic Church.

By simple logic of elimination, that leaves only the Catholic Church. Further, the Catholic Church can produce records tracing back to Apostolic times.

Therefore, I conclude that the Church described in Scripture is the infallible Catholic Church.

What do you think?