Why do we remain silent in Catholic Churches?
Assuming that what is being said is not itself sinful, it is morally neutral to talk. However, Catholic moral teaching tells us that "circumstances" change the moral character of actions.
Talking in Church when not demanded by necessity is at least venially sinful for the following reasons:
1) It is the Lord's House, which Jesus taught was "a house of prayer" (Mt 21:13) and thus should be used according to its purpose. This is a violation of justice against God, for whom we should have reverence.
2) It is a violation of justice against actual neighbors who are trying to pray. Again, necessity permits talking, just as it permits practicing the music before Mass and so on. However, most conversations are trivial and could gone on elsewhere at another time. This puts them in the category of unnecessary. The truth of this is shown by the strict guard for silence maintained in the chapels of the Roman basilicas where people are praying. Even in the areas where the tourists are viewing the architecture and art, talking above a whisper is not permitted. This is an accurate reflection of the Catholic respect for the church and for others.
3) Finally, it is a violation of charity, since as Christians we should be going "out of ourselves" to look after others first. If a person crassly and knowingly disregarded others trying to pray, or worst of all did so with malice or contempt, it could even be a mortal sin against charity.
These are basic principles of Catholic moral theology and need no other authority than that.
Sometimes a friend approaches us after Mass and wants to start a conversation with us. It is appropriate for us to invite them outside of the Church, into the gathering space, for that conversation. We give a great witness to our fellow Catholics when we first lead by example. Sometimes we want to greet a new family that has joined our parish, this is a very good thing for us to do to show our hospitality, quietly invite them to the gathering space and greet them there. We should always welcome our new parishioners, but we should remember that our respect and reverence for Jesus in the Blessed Sacrament comes first.