Jesus, friend of women, did not miss an opportunity to elevate the status of women, while at the same time illustrating the fallacy of gender-based-role-religion.
In Matthew 16:15-18 and Matthew 7:24, using as examples Peter, the Ek-klesia (the Out-Called Body of Christ), and obedience to the Written and Revealed WORD OF GOD, he obliterates all notions the apostles may have harbored of male headship.
In Matthew 16:15-18, Jesus asked his disciples, "...whom say you that I am And Simon Peter answered and said you are the Christ the Son of The Living God And answering Jesus said Blessed are you Simon son [of] Jona for flesh and blood has not revealed this to you but my Father which is in Heaven And I say also to you That you are Petros  but upon this "THE" Petra  I shall build [my home]  the Ek-klesia and the gates of hades shall not prevail against it (see Matthew 7:24).
 Jesus called Peter a petros (Strong's G4074), which is the same as G4075, meaning a proper masculine noun for a piece of a stone, a piece of a rock, or a man's name.
 Jesus called his Ek-klesia, "THE" Petra [Strong’s G4073]. The "THE" is present in the Greek but inexplicably left untranslated by scholars. Petra is a feminine noun meaning a massive living rock: th πέτρα THE pétra.
According to James Strong, pétra is the feminine counterpart of the masculine name petros. Strong claims that petra , the massive living stone, is the same as petros [G4074 and G4075] a piece of rock. But this is not true, and he had to know this.
The feminine noun Petra (G4073-the massive living stone upon which the Body of Christ is built) is not the feminine counterpart of the masculine noun petros (G4074-the piece of rock). James Strong allowed his prejudice in favor of gender-role-religion to influence many of his definitions, and this is one of them.
Simon's name, petros [G4074], means a little stone—a piece of a rock. It is the same word as petros [G4075], which also means a little stone—a piece of a rock. The two words, G4074 and G4075 are one and the same word. They are identical...separated only by the whim of James Strong.
Strong does this more than once. He does it with the word 'āḏām (pronounced, in Hebrew, as audawm). 'āḏām is the name God bestowed on all mortals at the time of their creation, "...male and female created he them and called their name 'āḏām (Genesis 5:2)."
Petros and 'āḏām are just two examples of the same Greek word being given two different Strong's reference numbers when one would have served better.
James Strong erroneously defined the word petra (G4073) as the female counterpart of the word petros [G4074 and G4075]. Strong and other scholars know full well this is not the case. In Matthew 7:24, Jesus used the feminine petra (G4073)], when commanding believers to build their homes on THE Petra [on "THE" Rock] instead of building on sand.
Using gender specific words within the context of Matthew 16:18 and Matthew 7:24, Jesus illustrates the difference between the masculine petros [a piece of a stone] and the feminine "THE" Petra ["THE" massive living rock].
In their fierce struggle in defense of gender-role-religion, traditional scholars wrestle with the feminine word petra being preeminent over [and much stronger than] the masculine word petros. Using both the Body of Christ (the Ek-klesia) and the man, Peter, Jesus' illustration obliterates the fallacy of gender-based-male-headship-role-religion.
The MASSIVE living--feminine--petra is much stronger than, and has preeminence over, the smaller pieces of the rock, the [male] petros.
This writer is not attempting to assert gender authority here, just making a point.
 The phrase Jesus used “I shall build” comes from the Greek compound word, oiko-domEsO/oiko-domeō, which means homebuilder in the physical, spiritual, and emotional senses.
When reading these words, the English word, "domestic," as in "home" comes to mind.
The English word, domestic, descends directly from the Latin word domesticus but is very similar (in both sound and meaning) to the Greek words domeso or domeō. Latin was the original language of the ancient Romans. They adopted Greek culture and language later, so it would be ludicrous to claim there is no linguistic connection between words that come from cultures that blended and used words so similar as domestic, domeso, domeo, and domesticus.
In the Ek-klesia, Jesus is building a domestic home for himself.
The Greek word he used, oiko, means “house or home.” The domeo/domeso part means to [physically and domestically] build houses or homes by building the dwelling itself and by edifying and building up those who live within the dwelling.
The Ek-klesia is the home that Christ is domestically building for himself. In my Father's House are many mansions. The building materials he uses are love and the living stones of each believer, who he instructs to build their homes upon the massive, living, and feminine...petra.
The strong, preeminent, and feminine petra is the revealed WORD OF GOD –Matthew 7:24 and 16:18.
Traditional-role-religionists deliberately obscure [where they can] the meanings of biblical words that expose the unscriptural paradigm of male headship.
The Bible is a treasure-trove of eye-opening subtleties and sub-text, if we will but make the effort to search them out.
If God intended his male creation to be preeminent over his female creation, then, despite the androcentricity of the Greek language, why did Jesus choose gender-specific language favoring the feminine in that particular discourse with Peter?
Why did our Creator allow the language itself to subordinate the masculine little piece of a rock [petros] to the massive rock, the living and preeminent [but God forbid--feminine], petra?