Egalitarian theologians have been able to find many weaknesses within complementarian theology. It is important to understand how complementarians think, what biblical arguments they stand on, and why they continue to hold to their founding principles.
Complementarians are generally extreme respecters of the Bible. They take most of what it says literally and truly believe they hold the most accurate understanding and interpretation. In my experience, they tend to be very logical thinkers and struggle with thinking outside the box. One can see why certain personalities would be drawn to this movement and likewise, why certain personalities would be repulsed by this movement.
If an egalitarian appears to not respect the Bible consistently, the complementarian will normally disengage from the conversation. This is why it is imperative for egalitarians to remain faithful to the authority of the Holy Scriptures when arguing for gender equality.
Complementarians place all their chips on 1 Timothy 2:12, which states,
“I permit no woman to teach or to have authority over men; she is to keep silent” (RSV).
This verse is the “complementarian trump card” and many will not even bother bringing up other verses to support their arguments. They may also mention Ephesians 5:22-23 or 1 Corinthians 14:34-35, but to the literal complementarian, no other verse other than 1 Timothy 2:12 is needed to prove their case.
The best chance we have of convincing complementarians that God has called women to lead in the church is by providing undeniable biblical evidence of women who did just that.
Egalitarians, who are often great respecters of the Bible as well, have gone to great lengths to explain the appropriate meaning of these three Bible passages within historical and biblical context, but some complementarians do not seem able or willing to accept these arguments.
While it is important that we continue to lay out egalitarian evidence concerning these three controversial Bible passages for those who are seeking answers, it is unlikely that we will convince complementarians on these grounds alone.
In my opinion, the best chance we have of convincing complementarians that God has called women to lead in the church is by providing undeniable biblical evidence of women who did just that.
There are seven named female church leaders named in the Pauline letters (Prisca, Euodia, Syntyche, Phoebe, Apphia, Chloe, and Junia), but complementarians have found ways to dismiss them all as women who only led other women, women who ministered under the authority of men, or women who simply did not exist.
The most significant female leader found in the Pauline letters is the apostle Junia, since being an apostle was the greatest of church offices at the time. Romans 16:7 states, “Greet Andronicus and Junias, my kinsmen and my fellow prisoners they are men among note of the apostles and they were in Christ before me” (RSV). The name Junias is translated Junian in the accusative form. Junian could be translated either as Junias, which is masculine, or Junia, which is feminine.
In the past, translators have assumed Junias was a man, but the new RSV has translated the name as the female Junia. There are several reasons for this change. One, the name “Junia” is a common female name in historic Latin and Greek literature and inscriptions, while “Junias” is not. Second, the writings of the patristic era exhibit the name as Junia, a female apostle. Further, the words “men” and the “men” of “kinsmen” are not even in the Greek text, according to the RSV translation. 
However, even with a substantial amount of evidence that Junia was in fact female, complementarians easily dismiss her because her female identity had been hidden for a century.
Eldon Jay Epp, professor, biblical scholar, and author of Junia: The First Woman Apostle, remarks:
“For me—and those like-minded—the task that lies ahead is to make only one of these corrections, and to make it stick: Junias must be corrected to Junia. I trust that both theoretically and actually the Apostle Junias, who had deprived Junia a century of apostleship—has evaporated—and rightly so—for he was merely the figment of the wishful imagination of some influential white European, British, and American male scholars, caught up in but actively abetting a culturally shaped bias that wished to exclude women from leadership positions in the church-in this case a role that a named woman filled in the earliest period and fulfilled as an outstanding member.” 
Epp’s findings concerning Junia are astounding. This is usually sufficient evidence to convince egalitarians and seekers alike, but complementarians continue to remain unconvinced and unimpressed.
However, egalitarians have a “trump card” too and her name is Deborah. Complementarian co-founder, John Piper, has found Deborah to be an “exception to the rule” and has sought to downplay her role as judge over the Israelite army. Yet, there is some compelling evidence that even the most logical and literal complementarian cannot ignore.
John Piper and many complementarians claim to be Reformed Calvinists. This systematic and extensive theology was founded by John Calvin, a pastor and well-known theologian in the 1500s. Calvinist theology can be simplified with the following five points:
T – Total depravity
U – Unconditional election
L – Limited atonement
I – Irresistible grace
P – Perseverance of the saint
For the sake of this argument, I will focus on the fourth point: “irresistible grace.”
In John Piper’s online article entitled, “What We Believe about the Five Points of Calvinism,” he states:
“The doctrine of irresistible grace does not mean that every influence of the Holy Spirit cannot be resisted. It means that the Holy Spirit, whenever he chooses, can overcome all resistance and make his influence irresistible.” 
It should be noted that John Piper is describing how one converts to Christianity in this text, but Calvinists apply “irresistible grace” to all aspects in life. In simple terms, if God wants someone to do something, he can most certainly compel them to do it, whether they want to or not.
Egalitarians have a “trump card” too and her name is Deborah.
In another one of John Piper’s online articles entitled, “The Womanliness of Deborah,” he states:
The question arises, where are the elders and priests whom God had appointed to judge the people (Exod 29:9; Num 11:16-25)? The only priest mentioned in the book of Judges is apostate (Judges 17-18). The elders after Joshua’s time are corrupt or foolish (Judges 2:7, 10; 8:14-16; 21). Likely, the people resorted to Deborah because she had both the word of God and personal integrity, a rare combination in those days. 
The question that Reformed Calvinists and complementarians should be asking themselves is this:
If Deborah was not God’s first choice to lead as judge of the Israelite army, if she was a leader God merely “resorted to,” then why did he not use his “irresistible grace” to raise up a man to do the job?
The only logical explanation a Reformed Calvinist could give is that God simply did not want to. But this leads us to the question, why would God not want to? Was he trying to prove to the Israelites how evil they were and if so, why would God allow the Israelites to win the battle under Deborah’s command?
Although Piper could argue that God wanted to disgrace the Israelite men who failed to lead by allowing a female leader to succeed, this would be a far reach even for him.
Piper and his followers can continue to be Reformed Calvinists or they can continue to be complementarians, but they cannot continue to be both if they cannot answer this simple question.
 Keith A. Gerberding. “Women Who Toil in Ministry, Even as Paul” (Southgate): 288.
 Eldon Jay Epp. Junia: The First Woman Apostle. (Minneapolis: Fortress Press, 2005): XVII.