Your post proves nothing.
Clement believed they were instructions, to the point where he said:
If anyone disobey the things which have been said by him [God] through us [i.e., that you must reinstate your leaders], let them know that they will involve themselves in transgression and in no small danger. .
My question to you: Why did Clement feel he had authority over the Church at Corinth?
Other examples of Papal authority being exercised in the first three centuries after Christ:
Pope Clement (88-97) wrote to the Church in Corinth in the year 96 to tell them to make changes in their attitudes and practices. The Early Church On-Line Encyclopedia (Ecole) Initiative, a cooperative effort on the part of Catholic, Orthodox, and Protestant scholars across the Internet to establish links of early Church history, says "This letter is important because it indicates that the author was acting has
the head of the Christian Church and that it was centered in Rome."
Pope Victor (189-199) ordered Easter to be celebrated throughout the world on Sunday, rather than on the 14th Nisan, whichever day of the week it happen to fall. All of the churches adopted Easter Sunday except those in Asia Minor. Pope Victor then excommunicated all the bishops in Asia Minor. While the Pope eventually relented in the excommunication, no one ever suggested that he did not have the authority.
Pope Calixtus (217-222) overruled those bishops who excommunicated for life all apostates, adulterers, and murderers, regardless of their repentance. The Pope decreed that all sinners with contrition could be absolved and received back into the Catholic Church.
After Pope Cornelius (251-253) was elected, he was faced with an antipope, Novatian, who promptly went about trying to consecrate bishops throughout the world who would be loyal to him. Naturally, this created tremendous uncertainty and confusion wherever Novatian tried to create false bishops over the heads of the legitimate bishops. This unequivocally shows the power of the Pope as the recognized leader of the worldwide Catholic Church.
Pope Stephen (254-257) removed certain bishops in Africa for heresy. Later he overruled a synod of African bishops which wanted to re-baptize lapsed Catholics returning to the faith and those converting to Catholicism from schismatic sects. The Pope made it very clear he was in charge and eventually prevailed in this matter.
Pope Dionysius (260-268) reprimanded Bishop Dionysius of Alexandria for misstatements on the Trinity. The Bishop then followed the Pope’s guidance.
Pope Sylvester (314-335) did not attend the First Council of Arles (314), thinking it unbecoming for him to leave Rome. Following Arles, the bishops there commended him for not leaving the spot "where the Apostles daily sit in judgment." He repeated this example at Nicaea, which his successors followed in the councils of Sardica (343), Rimini (359), and the Eastern ecumenical councils. At Nicaea, Pope Sylvester sent two priests as his legates, who helped preside over the sessions and who were the first to sign the cannons.
Pope Julius (337-352) decided that Athanasius, rather than Pistus, should be the Bishop of Alexandria. At the same time, he read the riot act to the Arians in Alexandria.
Because Pope Liberius (352-366) stood firm against Arianism, Emperor Constantius had him kidnapped and replaced with an antipope, Felix, who no one accepted. In captivity, the Pope was tortured until he signed a semi-Arian document, which, of course, was not valid. This episode clearly showed the vital role of the Pope in determining Catholic doctrine. The Pope returned to Rome and continued his fight for orthodoxy. He eventually succeeded in seeing many Arians come back to the Catholic Church.