CHALLENGERS AGAINST THE POSTER
So say you. How can you forget about the women in the Bible who were appointed as leaders in the church -- in the Old AND New Testaments???? It's alright for you to have your "preference" of a man over a woman, but don't try and make your preference a matter of scripture, because it isn't!
This topic is very challenging and many get emotionally charged about this sensitive issue. For those reasons, I am going to take this topic on slowly and deal with it in a couple of posts in serial.
This first post will try and get to the bottom of what Paul is saying to the Corinthian church about this topic in 1 Corinthians 14.
To begin with let's set the stage for when this letter was written and try to get some contextual understanding. In 1st century Judaism, women were not allowed into it to worship with the men but had to stay in the court of women at the temple or outside the synagogue. They listened in to the rabbis but learned from their husbands at home.
After Jesus was crucified, the Bible teaches us that the the veil surrounding the Holiest of Holies (where high priest would commune with God before the Ark of the Covenant) was rent (torn) in twain (two) at the crucifixion, signifying to all people that the way to God was now open to all men and women alike, as demonstrated by Paul's letter to the Galatians 3:28 which states "There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus." The men in leadership in Corinth wanted to preserve that tradition of the women being silent.
The big challenge in the new church at Corinth was that women were now allowed into the congregation and the church of Corinth was having problems keeping order in their services. (1 Cor. 14:40) They therefore came up with the rule cited by Paul in chapter 14 verses 34-35 to manage the problem along the lines of how they handled it in the temple and synagogues.
Therefore, Chapter 14:33-38 can be read in two ways:
1) That Paul is speaking literally on principle saying women should be silent as suggested in the provocative meme posted above, or
2) We can realize that verses 34-35 are a rhetorical quote, to which Paul is responding with sarcasm and admonition in verse 36. "What? Did the Word of God originate with you!?"
That is to say he finds that the unique Corinthian teaching of verses 34 and 35 that he is quoting, both outlandish and arrogant, telling them to stop teaching that on Paul's authority. verse 39 he mentions "sisters" signifying that he does mean to allow women the space to prophesy in church, and thereby address the congregation.
This interpretation is called a QRD or Quotation-Refutation-Device
Verse 36 provides the clarity needed. Paul is mocking and undermining that teaching he quotes in 34-35 telling the leaders in Corinth in verse 36 basically "Who are you to make such a rule as though the Word of God only came to you (men) alone?!"
(As an aside for my cessationist friends, this passage also reminds us NOT to forbid speaking in tongues, simply that all means of address should be done in a fitting and orderly way as Paul laid out in the preceding verses.)
If verse 36 was not present, #1 would be correct. But verse 36 points us to #2.
Then again, 1 Timothy 2 does point us back to the principles found in interpretation #1 leaving verse 36 challenged.
1 Timothy 2
11 A woman (wife) should learn in quietness and full submission.
12 I do not permit a woman to teach or to assume authority over a man (over her husband); she must be quiet.
13 For Adam was formed first, then Eve.
14 And Adam was not the one deceived; it was the woman who was deceived and became a sinner.
15 But women (she) will be saved through childbearing—if they continue in faith, love and holiness with propriety.
To get to the bottom of it all we really need to look at the original greek manuscripts and see where or whether there is punctuation because the literal greek renders the passage either of two ways providing very different results for 1 Cor 14:34-35:
"hai gynaikes en tais ekklesias sigatosan ou gar epitrepitai autais lalein alla hypotassesthosan kathos kai o nomos legei..."
"hai (the) gynaikes (women) en (in) tais ekklesias (the churches) sigatosan (let them be silent) ou (not) gar (for) epitrepitai (it is allowed) autais (to them) lalein (to speak) alla (but) hypostassesthosan (to be in submission) kathos (as) kai (and) o (the) nomos (law) legei (says)..."
EITHER A OR B IS CORRECT
A. "The women in the churches, let them be silent. For it is (not) allowed for them to speak but to be in submission..."
B. "The women in the churches let them not be silent for it is allowed for them to speak but to be in submission..."
Same words, moving the punctuation gives us one scenario where women can't speak at all and a second scenario where they can - but in both scenarios under the authority of men. verse 39 agrees with rendering B because Paul says that sisters can prophesy but done decently and in order.
Paul's common style is to make a thesis and then restate it after some explanatory content.
Syntax A is also grammatically awkward, and Syntax B is more in keeping with Paul's typical semantic patterns.
. 
AI GYNAIKES EN TAIS EKKLASIAIS SIGATOSAN OU GAR EPITREPETAI AUTAIS LALEI ALLA HYPOTASSESTHOSAN KATHOS KAI O NOMOS LEGEI
EI DI TI MAHTHAIN EIN DE THELOUUSIN EN OIKO TOUS IDIOUS ANDROS EPEROTATOSAN AISCHRON GAR ESTIN GYNAIKI LALEIN EIN EKKLESIA
E APH HYMON O LOGOS TOU THEO EXELTHEN EI EIS HYMAS MONOS KATENTESEN
AI GYNAIKES EN TAIS EKKLASIAIS SIGATOSAN OU GAR EPITREPETAI AUTAIS LALEI EIN ALLA HYPOTASSESTHOSAN KATHOS KAI O NOMOS LEGEI
EI DI TI MATHAIN THELOUUSIN EN OIKO TOUS IDIOUS ANDRAS EPEROTATOSAN.
36) E APH HYMON O LOGOS TOU THEO EXELTHEN EI EIS HYMAS MONOUS KATENTESEN
This link below is a well researched article that tends challenges my Quotation-Response Rhetorical Device theory. The author has provided some solid research trying to show that QRD is not the rhetorical device in use here. I am not yet inclined to agree with him, but the case is somewhat compelling.
https://www.cbeinternational.org/resource/1-corinthians-1434-35-marginal-comment-or-quotation-response-kirk/