I deal with the subject of Male Headship in a separate article whose link is given in the reference section. Here consideration is given to the subject of biblical typology and its proper use with respect to male headship.
Some people use improperly the biblical interpretation tool of biblical typology (type and antitype) to incorrectly invalidate the male headship principle.
The type/antitype tool is based on the biblical use of figures as in Romans 5:14 and Galatians 4:24. It is a useful tool in some scriptural contexts. However, like any other tool, it can be used improperly.
Generally, type refers to an Old Testament person, place, or thing to include events, concepts and principles. On the other hand antitype refers to such in the New Testament that strongly relates to the type in the Old Testament. Type in the Old Testament is said to foreshadow, prefigure, and point to the antitype in the New Testament.
An article that improperly employs biblical typology to invalidate headship is given at the link below.
The following observations are made concerning the article.
The article claims that in Romans 5:12-21, the word Adam is used as a type for humankind (male and female, both Adam and Eve) rather than referring to the male Adam.
Romans 5:19 says by ONE disobedient man many were made sinners; by ONE obedient man many are made righteous.
Romans definitively answers the question of why it is sound doctrine to say God holds Adam primarily responsible for the initial sin.
Moreover, the scriptural principle that the conception of the baby Jesus did not involve the male spiritually tainted seed is one of many examples of the biblical pattern of male primary responsibility assigned by God by spiritual design though it may be intellectually counterintuitive and undesirable by some humans.
The use of the word man instead of human is used in the KJV since it was understood in the translators days and now that the word man is generic for human being in this context and some other contexts.
Indeed, the word Adam in the Hebrew language is used for humankind precisely since all humans including the female derived from the male Adam.
So in Romans 5:12-21, Paul is not using the word Adam as used in Genesis 1:26-27. He is using it as used in Genesis 2:7. Context informs as to whether the general or specific is meant; this includes Romans 5:12,14 where the person is clearly the specific human the male Adam.
This generic use of the word man is biblically consistent that Paul speaks of the male Adam.
So even if the KJV translators had used the word human, that would not have changed the truth that Paul speaks of the male Adam in Romans 5.
Moreover, the use of the numerical word one and the use of the numerical word many in contrast to one another establishes that Paul is not including the numerical two (couple Adam and Eve) but rather only the male Adam.
Clearly the male Adam was the first human and all his descendants are accounted by God as sinners until the advent of the crucified Christ.
Now then this all necessarily includes Eve as she came from this first human, the male Adam.
So then it is by God’s spiritual design that he has established primary responsibility for human race sin as a whole though he yet holds each person responsible for his/her own sin.
Therefore it is by God’s spiritual design that the taint of sin (sin nature) is inherited from the male seed.
By God’s spiritual design, if Jesus had come through the male Adam, Jesus would not have been holy from the womb. It is as God designed it for his own consistent plan/purpose.
1 Corinthians 15:21-22,45 support the observation that Paul in Romans 5 refers to the male Adam:
21 For since by man came death, by man came also the resurrection of the dead.
22 For as in Adam all die, even so in Christ shall all be made alive.
45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
Article is at Is Adam Solely Responsible For The First Sin