He doesn't. He questions the idea of the papacy as a monarchy, which the Pope was; for centuries he headed a civil state. Did Jesus intend for the Pope to head a state?
Vatican II wrestled with the place of the Pope and came up with the term collegiality, with the Pope as first among equals.
He also attacks Papal infallibility.
Papal infallibility has been exercised three times: the dogmas of the Assumption and Immaculate Conception of Mary were defined infallibly, but had been held by Catholics for nearly 2000 years. So, these definitions were a bit redundant.
The third time it has been used was in 1870, when the dogma of Papal infallibility itself was defined.
Popes themselves are reluctant to invoke it; Paul VI specifically crossed out the word "infallible" in Humanae Vitae, and John Paul II has not formally defined anything infallibly either.
If you find yourself agreeing with this article as you read it, you have no idea what the Catholic Church is all about -- just like the author.
I do find myself agreeing with the author's historical perspective of celibacy because, in fact, it is correct.
He also attacks Papal infallibility. I'd say that's anti-Catholic.
Was John XXII, fondly referred to as the "whore of Avignon" and whose reputation was so sullied no one would take his papal name for the next 700 years, infallible? Was St. Peter, who denied Christ three times, infallible? Again, this is a doctrine which was promulgated by men 1900 years into the Church's history. The Church has had theological debates over such issues throughout its existence. Just because someone differs with you doesn't make them "anti-Catholic" any more than the debate over the poverty of Christ rendered either of the opposing sides "anti-Catholic."
I suspect you agree with the author though.
So what? That is only an assertion ad hominem and not a valid deconstruction of the arguments presented.
William of Occam would grab you by the ear and tell you to get thee to a Jesuit for some schooling in the trivium.
I don't think he questions whether Christ founded his Church on Peter. He is just saying that he does not believe that Christ intended that Peter (or the Pope) become an absolute monarch.
As for attacking the Pope's infallibility, you're right. That makes him a Protestant because the Infallibility of the Pope in matters of religion is an article of faith in the Catholic Church. You can't pick and choose. You have to buy the entire package.
That's one reason I'm a Protestant. Catholic doctrine has changed over the years. That means that either the current Pope is wrong about a matter of religion or a former Pope was -- since I don't believe that God is changing His mind. Therefore, I cannot believe in the infallibility of the Pope. It is a logical impossiblity.
As for the rest, I really don't care if Catholic priests are celibate. There's no scriptural basis for the requirement, but it's your religion. You can do what you want and there is a great deal to be said for tradition.
I will point out that I do not believe that the media attacks are really about allowing priests to marry. That's just phase 1. Next it will be allowing priests to be openly homosexual. That's the real agenda.