If someone used logic to determine truth, should we always follow him? Did not Socrates come up with logical conclusions that were seemingly irrefutable? All Socrates proved and all you have proven is that men can build a house that appear to us to be quite solid. So it is with the Catholic Church. They have found an answer for nearly every question a man might ask, and present then their finished product as the one and only true church. Have they done a better job than the leaders of Judaism in the time of Jesus?
No, the Jews has gone astray from the Spirit of the teachings of God as well as missing the letter of what was written in the scripture. The Catholics as a group have done worse for they have had more at their beginning than did the Jews. The follow verse explains the problem for those who are able to understand it:
"But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more. " Luke 12:48
The Baptist made it clear to those with eyes to see and with ears to hear:
"I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:" Matt 3:11
Individuals within the group [the CC and the RCC] have followed the Way of Jesus, but the larger group which names itself as God's Church has missed the most important thing. They know many of the right words, but there is for the most part no Spirit and therefore no Life in it. How can the Body of Christ be dead? He was dead, but the three days are past. He has resurrected. The Holy Ghost has been poured out on whosoever will.