How is "binding and loosing" extrapolated to all clergy? Matthew 16:19
  And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.


I recently read an article in which the Roman Catholic author states, 


  In the Catholic Church’s understanding, the office of “binding and loosing” which was given to Peter was also assigned to the whole college of apostles who in turn commission their assistants in ministry to do likewise.


If it is understood that Jesus was talking to Peter, by what rationale or authority can this "office" be passed on from him to others?
Christ gave St. Peter the "power of the keys" to bind or loose.

Addressing the question of "Whether priests alone have the keys?," St. Thomas Aquinas writes:


  There are two kinds of key. One reaches to heaven itself directly, by
  remitting sin and thus removing the obstacles to the entrance into
  heaven; and this is called the key of "order." Priests alone have
  this key, because they alone are ordained for the people in the things
  which appertain to God directly. The other key reaches to heaven,
  not directly but through the medium of the Church Militant. By this
  key a man goes to heaven, since, by its means, a man is shut out from
  or admitted to the fellowship of the Church Militant, by
  excommunication or absolution. This is called the key of
  "jurisdiction" in the external court, wherefore even those who are not
  priests can have this key, e.g. archdeacons, bishops elect, and others
  who can excommunicate. But it is not properly called a key of heaven,
  but a disposition thereto.


Addressing the question of "Whether holy men who are not priests have the keys?," St. Thomas explains why only those men ordained to the priesthood have the power of the keys:


  There is this difference between a principal and an instrumental
  agent, that the latter does not produce, in the effect, its own
  likeness, but the likeness of the principal agent, whereas the
  principal agent produces its own likeness. Consequently a thing
  becomes a principal agent through having a form, which it can
  reproduce in another, whereas an instrumental agent is not constituted
  thus, but through being applied by the principal agent in order to
  produce a certain effect. Since therefore in the act of the keys the
  principal agent by authority is Christ as God, and by merit is Christ
  as man, it follows that on account of the very fulness of Divine
  goodness in Him, and of the perfection of His grace, He is competent
  to exercise the act of the keys. But another man is not competent to
  exercise this act as principal agent, since neither can he give
  another man grace whereby sins are remitted, nor can he merit
  sufficiently, so that he is nothing more than an instrumental agent.
  Consequently the recipient of the effect of the keys, is likened, not
  to the one who uses the keys, but to Christ. Therefore, no matter how
  much grace a man may have, he cannot produce the effect of the keys,
  unless he be appointed to that purpose by receiving [holy] orders
  [(the priesthood)].


Thus, your question really amounts to why St. Peter and his successors, the popes, are necessary for there to be a valid priesthood.