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Christ is clearly continuing to refer to Peter.

This “little rock” vs. “big rock” nonsense is tortured linguistics, intended to ignore Christ’s clear meaning.

This and the rest of your argument would have us prefer YOUR “infallibility”, over that assigned by Christ Himself.

It's not tortured linguistics. Failure to correctly translate the original Greek, which makes the distinction, is the problem

The problem is basing an entire doctrine on one mistranslated verse.

Petra – Peter rock

Matthew 16:18 - http://bible.cc/matthew/16-18.htm

Jesus said that Peter was *petros*(masculine) and that on this *petra*(feminine) He would build His church.

Greek: 4074 Pétros (a masculine noun) – properly, a stone (pebble), such as a small rock found along a pathway. 4074 /Pétros (”small stone”) then stands in contrast to 4073 /pétra (”cliff, boulder,” Abbott-Smith).

“4074 (Pétros) is an isolated rock and 4073 (pétra) is a cliff” (TDNT, 3, 100). “4074 (Pétros) always means a stone . . . such as a man may throw, . . . versus 4073 (pétra), a projecting rock, cliff” (S. Zodhiates, Dict).

4073 pétra (a feminine noun) – “a mass of connected rock,” which is distinct from 4074 (Pétros) which is “a detached stone or boulder” (A-S). 4073 (pétra) is a “solid or native rock, rising up through the earth” (Souter) – a huge mass of rock (a boulder), such as a projecting cliff.

4073 (petra) is “a projecting rock, cliff (feminine noun) . . . 4074 (petros, the masculine form) however is a stone . . . such as a man might throw” (S. Zodhiates, Dict).

It’s also a strange way to word the sentence that He would call Peter a rock and say that on this I will build my church instead of *on you* as would be grammatically correct in talking to a person.

There is no support from the original Greek for the idea that Jesus meant Peter to be that which He was going to build His church on. The nouns are not the same as one is feminine and the other masculine and denote different objects.

In first century Greek, petros and petra did not mean “small stone” and “large rock.” The terms did have those meanings in some early Greek poetry, but by the first century, this distinction was gone and the two were synonyms (EBC 8:368).
Furthermore, “the Aramaic kepa, which underlies the Greek, means ‘(massive) rock’” (EBC 8:367), not “small stone.”
The usage of the two different terms if fully accounted for by stylistic variation. Too much repetition grates on the ears, which is the whole reason we have pronouns—to avoid excess repetition. In this case, varying the term petros as petra is a normal stylistic variation to avoid repetition in the same sentence.
We would acknowledge even greater examples of stylistic variation in everyday speech in English. If I were a hospital administrator attending a fund-raiser where I planned to announce that one of my chief doctors, a man named Dr. Robert Stone, would be the chief physician of a new wing of the hospital, I might publicly say, “I tell you truly, Bob, that you are a Stone, and on the rock I will build a whole new wing of the hospital.” Nobody at the function would think I was referring to anyone except Dr. Stone as the rock on which the new wing is built. It is perfectly normal stylistic variation, and the etymological difference between the English terms “stone” and “rock” is ever greater than the difference between the Greek terms “petros” and “petra.”
Even supposing, contrary to the linguistic evidence, that the two terms should be read as “small stone” and “large rock,” this does not mean Jesus is diminishing Peter in the statement. The anti-Petrine argument assumes that, if there is a difference in the two terms, there must be antithetic parallelism between the statement about Peter and the statement about the rock. I.e., that Jesus is diminishing Peter by contrasting him with the rock: “I tell you Peter, you are a very small stone, but on the great rock of my identity, I will build my Church.” However, the assumption that the parallelism is antithetic is merely an assumption with no proof. It can just as easily be synthetic, so that the statement about the rock expands on the statement about Peter: “I tell you Peter, you may look like a small stone now, but on the great rock you truly are, I will build my Church.”