So to put it simply: Private interpretation is wrong. The option now being to privately interpret church history and scripture to conclude which infallible or ultimate church authority to pick. Catholic, Orthdox, Coptic, JW… All claim in some way to be the true church and expression of it.
Hope this does not sound sarcastic, not my intention

just genuine thoughts I have on this.
Regards
Lincs
First, let me ask you…prior to 1521, the protestant reformation…someone, wanting to join Christianity…which church would that person join?
Let us bring it back further…in 1000AD…which Christianity would you join? in AD800? in AD500?
Hmmm…but there is a guide from Scripture. Let me point them out to you:
from Luke…Luke 10:16 (Douay Rheims)
16 He that heareth you, heareth me; and he that despiseth you, despiseth me; and he that despiseth me, despiseth him that sent me.
Let me cite the example of St. Paul:
Galatians 2:2 I went in response to a revelation and, meeting privately with those esteemed as leaders, I presented to them the gospel that I preach among the Gentiles. I wanted to be sure I was not running and had not been running my race in vain.
Paul had a direct revelation from Christ. Yet, from the two passages above, he goes to visit Cephas/Peter and submits himself to Peter. Gal 2: 2 states his purpose…to present his gospel/message to make sure it is in line with the Apostles and what they were handed down from Christ.
This fulfills this: Then from 1John 4…6 We are from God, and whoever knows God listens to us; but whoever is not from God does not listen to us. This is how we recognize the Spirit[a] of truth and the spirit of falsehood.
Further…Then, Clement of Rome writes this in his Epistle to Corinth…in accordance with the passages above…
earlychristianwritings.com/text/1clement-lightfoot.html
57:1 Do ye, therefore, that have laid the foundation of the sedition submit yourselves to the presbyters, and be chastised to repentance, bending the knees of your hearts.
59:1 But if some should be disobedient to the things spoken by him through us, let them know that they will entangle themselves in no small transgression and danger,
Now look at Acts 13:
1 Now in the church at Antioch there were prophets and teachers: Barnabas, Simeon called Niger, Lucius of Cyrene, Manaen (who had been brought up with Herod the tetrarch) and Saul. 2 While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” 3 So after they had fasted and prayed, they placed their hands on them and sent them off.
Look at verse 3 and see what the Antioch Church elders do…“they placed their hands on them and sent them off.”
This fulfills the passage below:
Romans 10:
14 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them?
15 And how can anyone preach unless they are sent? As it is written: “How beautiful are the feet of those who bring good news!”[g]
Before Paul and Barnabas went on their first missionary journey, he submits himself to Church authority and are ordained by laying of hands. Then they are sent out to their mission. Paul, by the laying of hands, first becomes an Apostle, he gains apostolic authority, thereby, the Churches he founds have apostolic succession.
In other words…know who “sent” the preacher you are listening to?
The Catholic, since the time of the Apostles…have been practicing this. Again, I will cite Clement of Rome…
1Clem 42:4 So preaching everywhere in country and town, they appointed their firstfruits, when they had proved them by the Spirit, to be bishops and deacons unto them that should believe.
1Clem 44:2 For this cause therefore, having received complete foreknowledge, they appointed the aforesaid persons, and afterwards they provided a continuance, that if these should fall asleep, other approved men should succeed to their ministration.
Let me ask you then…Who sent Calvin? Who did he submit his message, his preaching to?
For all the other claimants as being the true Church…who fulfills the passages above?