In "Word Focus" Glenn McClure writes:

Verse 18 has been a source of controversy, and calls for a closer look. Here we need to ask the question, Does “this rock” refer to Peter, to Peter's confession, or to Christ? The contrast between Peter (petros) and rock (petra) sheds some light on the matter. Petros is a stone, loose and movable. It was used as a proper name and is used here in the masculine form. On the other hand, petra is feminine and therefore may not refer to Peter. Petra means a rock, immovable, like the one the wise man built his house upon (Matt. 7:24). Most Protestants, as well as some early Church fathers (Augustine, Jerome), feel that this refers to Peter's confession and not to Peter himself. This may be because this meaning had been abused by the Church of Rome, and therefore another meaning was sought. Yet from verse 23 we realize that Peter was neither the foundation nor the builder, but Christ alone, whom he had confessed (see also 1 Cor. 3:11).

Source: Building Christian Relationships: Adult Teacher's Insights, page 4.