The Church is built on the faith of St. Peter, so when his successor professes his faith it is infallible.
The Catholic Church IS the real Church.
Impeccability means sinlessness. The infallibility of the Church belongs to the Holy Spirit.
Whatever you shall bind on earth shall be bound in heaven and whatever you shall loose on earth shall be loosed in heaven.
Matthew 16:19;Matthew 18:18
What did Peter bind and loose on earth???