Peter as a male "rock"?

I was wondering why the translation of (paraphrasing here) “You are rock, and on this rock I will build my Church” includes a male Koine Greek word for the “rock” that Peter is, and then a female Koine Greek word for the “rock” that Christ’s Church is. I’m wondering if that translation forever leaves an opening for non-Catholic brothers and sisters to be able to question papal authority by asserting that if Peter was the rock that the Church was to be built upon, then the translation should’ve used the same word for “rock” for both Peter and the Church Jesus was commissioning.

 Why doesn't the translation just use the same word for "rock" so that there can be no confusion?  (I'm just trying to bolster my case for papal authority, and to make sure I've got all my bases covered for any possible future conversations.)

The following links should assist you in better understanding the Catholic Church’s teaching on Peter as the first Pope. If you have any further questions or concerns that are not answered by these links, please contact Catholic Answers directly.

**Recommended Reading:
*]Peter the Rock
*]Is Peter the Rock in Matthew 16:18?
*]You Can’t Get Past this Rock
*]The House Built on Rock

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