Certainly, the apostle Peter never claimed "divine lineage" - but the Vatican certainly does. The "Vicar of Christ" (or Vicarius Christi) literally means Substitute for Christ. The Vatican has been falsely claiming unique and divine authority for centuries that is a false interpretation of the words of Jesus. This was and is a human power grab of the authority of God.
As a Catholic, you must have known this answer before you asked me to clarify. I am not sure why you asked this question. Moreover, in my CCD and Catholic education, the supposed papal "unbroken link" of popes was a common lesson, as it was with my wife's Jesuit university education.
So what, exactly, do you mean by infallibility?
Let me ask you - who claims infallibility?
https://en.wikipedia.org/wiki/Papal_infallibility
You never addressed what I had to say in regard to the heresy of Francis. Here is a list containing some troubling things he has said or done.
http://thewildvoice.org/pope-francis-chronology-perspective/
What are Catholics to do when the very head of the church, the "Vicar of Christ" on earth - is clearly against the Word of God?
As a former Catholic (until my 30s), I can attest to this: until I asked Christ to come into my heart and submitted myself to Him, I never knew Him. Today, I have a real and incredible relationship with Christ that is the most profound thing I have ever experienced.
Actually, Vicar of Christ means "representative of Christ." The relationship is, in essence, the same as a "prime minister" to a king. I'm sorry if your CCD training and your wife's Jesuit college education taught you this falsely.
As a Catholic, you must have known this answer before you asked me to clarify.
Actually, I didn't know that you were implying that the pope claimed that he was a substitute for Christ. I was actually thinking that you were going to claim that Catholics believed that somehow he was divine. But I wanted you to clarify rather than making some sort of accusation.
Let me ask you - who claims infallibility?
Please try to answer the question that was actually asked. What do you mean by infallibility? I am particularly concerned that there may be a disconnect based upon a faulty definition.
As a former Catholic (until my 30s)…
As a former Catholic, you should be able to condemn the Church based upon the Church's own doctrine, provided your former status is based upon an actual doctrinal difference rather than receiving faulty education in that doctrine.
Proving Catholic doctrine false based upon what actual doctrine states will be far more effective for you rather than proving it based upon what you were taught or upon what some other "former" Catholic says. For example, if you say something along the lines of:
…you will probably have better luck than using the tactic of making a false accusation and then disproving that false accusation.
The reason being is if I know that your premise is false then I can utterly disregard your conclusion based upon that false premise. Certainly, you may be able to lead captive silly women laden with sins away from the Church (cf 2 Tim 3:6), but that is a testament more toward the poor state of catechesis within the Church rather than actual faults with Church doctrine.
BTW, you can cite whatever you'd like in regards to Pope Francis...but may I suggest that you actually look at trying to look for real references rather than citing a site that promotes the "visions" of a person named "Maria Divine Mercy"? Sort of hard to take such a thing seriously. You won't have any problems finding questionable quotes from him...you may as well use a legitimate source to do so.