...Firmilian's rhetoric is an early example of a sedevacantist argument. The very fact that the argument is made points to the reality of the institution of papacy, today, and in the 3rd century.
It seems to me that this is to assume the very thing in question; namely, was there any such thing as a bishop of bishops in the early church? What else can explain an interpretation of what was (to my knowledge) the very first recorded instance of a heretofore unheard-of demand by a Roman bishop that bishops of other Sees submit to his decrees, a claim that is excoriated to the point of ridicule, repudiated by the Eastern church, 86 bishops of the African churches, and the churches in Asia Minor as sedevacantist evidence of a papacy?
...he does so, interestingly, by disputing the validity of Pope Stephen's succession to the throne of Peter. He is not calling into question the institution of papacy at all.
Again, this is to assume the very thing in question, that is, that one particular bishop holds a position of authority over other bishops as head of the universal Church. Firmillian does not dispute Stephen's "succession to the throne of Peter" at all, because as the bishop of Rome he had that jurisdiction. However, since all Sees were viewed as possessing the throne of Peter, it is clear that he was repudiating Stephen's demand of obedience from his fellow bishops.
Cyprian, in a clear reference to Stephen, says in his opening remarks at The Seventh Council of Carthage,
...It remains, that upon this same matter each of us should bring forward what we think, judging no man, nor rejecting any one from the right of communion, if he should think differently from us. For neither does any of us set himself up as a bishop of bishops, 3 nor by tyrannical terror does any compel his colleague to the necessity of obedience; since every bishop, according to the allowance of his liberty and power, has his own proper right of judgment, and can no more be judged by another than he himself can judge another. 4 But let us all wait for the judgment of our Lord Jesus Christ, who is the only one that has the power both of preferring us in the government of His Church, and of judging us in our conduct there.
http://www.ccel.org/fathers2/ANF-05/anf05-124.htm
Cordially,
Firmilian, and other bishops may be disputing the institution of the papacy, but the very fact that they were doing it means that there was someone else who asserted it.
Cyprian's comment about the equality of bishops needs to be seen in the context of this quote:
4. If any one consider and examine these things, there is no need for lengthened discussion and arguments. There is easy proof for faith in a short summary of the truth. The Lord speaks to Peter,10 saying, "I say unto thee, that thou art Peter; and upon this rock I will build my Church, and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven; and whatsoever thou shalt bind on earth shall be bound also in heaven, and whatsoever thou shalt loose on earth shall be loosed in heaven."11 And again to the same He says, after His resurrection, "Feed nay sheep."12 And although to all the apostles, after His resurrection, He gives an equal power, and says, "As the Father hath sent me, even so send I you: Receive ye the Holy Ghost: Whose soever sins ye remit, they shall be remitted unto him; and whose soever sins ye retain, they shall be retained; "13 yet, that He might set forth unity, He arranged by His authority the origin of that unity, as beginning from one. Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity.14 Which one Church, also, the Holy Spirit in the Song of Songs designated in the person of our Lord, and says, "My dove, my spotless one, is but one. She is the only one of her mother, elect of her that bare her."15 Does he who does not hold this unity of the Church think that he holds the faith? Does he who strives against and resists the Church16 trust that he is in the Church, when moreover the blessed Apostle Paul teaches the same thing, and sets forth the sacrament of unity, saying, "There is one body and one spirit, one hope of your calling, one Lord, one faith, one baptism, one God? "17Treatise I. On the Unity of the Church
More quotes from Cyprian are at St. Cyprian on the Church and the Papacy, for example,
With a false bishop appointed for themselves by heretics, they dare even to set sail and carry letters from schismatics and blasphemers to the chair of Peter and to the principal Church [at Rome], in which sacerdotal unity has its source; nor did they take thought that these are Romans, whose faith was praised by the preaching Apostle, and among whom it is not possible for perfidy to have entrance.(Letter 55)