[MHGinTN]

No, your error is in not consulting the previous sentences Jesus spoke. It is a common error. Even Augustine understood that Jesus referred to what Peter spoke by the urging of the Holy Spirit, rather than Peter as what Jesus would build His EKKLESIA. Jesus was not speaking of building an institution. HIS CHURCH is spiritual, not an institutional edifice with the very thing HE condemned in The Revelation, a priesthood of an institutionalized system (Nicolai-tens).

[Fantasywriter]

In support of your statement that Jesus did not found an organization, here is the passage in which He specifies the nature of worship under the New Covenant [i.e.: it’s not location/organization-centered but spirit-and-truth-centered]:

John 4:

19 The woman said to Him, “Sir, I perceive that You are a prophet.

20 Our fathers worshiped in this mountain, and you people say that in Jerusalem is the place where men ought to worship.”

21 Jesus said to her, “Woman, believe Me, an hour is coming when neither in this mountain nor in Jerusalem will you worship the Father.

22 You worship what you do not know; we worship what we know, for salvation is from the Jews.

23 But an hour is coming, and now is, when the true worshipers will worship the Father in spirit and truth; for such people the Father seeks to be His worshipers.