What teachings of the Church are binding?

“Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it. And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose upon earth, it shall be loosed also in heaven. Then he commanded his disciples that they should tell no one that he was Jesus the Christ.”
           Matthew 16:17-20   
         Christ gave the Church the ability to bind the faithful to teachings of the church but that is not to say that all teachings of the Church are binding. As the Catechism of the Catholic Church puts it 
        “Jesus entrusted a specific authority to Peter: “I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.” The “power of the keys” designates authority to govern the house of God, which is the Church. Jesus, the Good Shepherd, confirmed this mandate after his Resurrection: “Feed my sheep.” The power to “bind and loose” connotes the authority to absolve sins, to pronounce doctrinal judgments, and to make disciplinary decisions in the Church. Jesus entrusted this authority to the Church through the ministry of the apostles and in particular through the ministry of Peter, the only one to whom he specifically entrusted the keys of the kingdom” ¹
        The first example we have of the Church exercising this power is in Acts 15 which describes the Council of Jerusalem. The council consisted of Barnabas, Paul, James the Just, Peter, and John. It had been called in order to discuss several issues but one being among them being the importance of circumcision. This is the first council in which an infallible teaching is enacted by Peter ².
         In today’s church though it seems like Catholics pick and choose the teachings of the church to follow. So how do we know which teachings are “binding”? All faithful are bound to believe and follow all doctrines, teachings, and dogmas defined as authoritative. 
There are two main ways for the Church to define authoritative teaching
1. By way of a ecumenical council or synod
2. By way of a papal ex cathedra statement(infallible statement)
        For an ecumenical council/synod teachings are binding if they’ve been officially defined. Councils can go on for a while and a lot of conflicting ideas can be thrown around so if you’re keeping up with what the Bishops are saying their statements are not considered infallible. When the council comes to a final decision they will make an explicit authoritative statement usually delivered by way of a public declaration and documentation. Papal ex cathedra statements (only two have ever been made) are a lot more rare and have 2 requirements.
1. Be made explicitly clear that it is intended to be an infallible statement by the Pope as the successor of Peter.
2. Be on a matter of faith or morals
 
        Now, there are several other types of Catholic teaching such as Catholic social teaching but these are not necessarily binding in their entirety unless defined through one of the two methods mentioned earlier.

¹CCC 553

²Acts 15:6-30