Grudem and Poythress, who are far more skilled on the issue than I, have already dealt with those passages in their "Gender-Neutral Controversy" book, pp. 306, 312, 314-15. Go argue with them...
I have not got much time, but I will briefly respond to Grudem and Poythress here, and show their bias in the arguments. I quote from the work that you mention:
"Johannes P. Louw and Eugene A. Nida, Greek-English Lexicon of the New Testament, 9.1, claim that
anēr has the meaning “person, human being, individual” in Matt. 14:35 and Romans 4:8 (they cite only
these two, but of course it is possible that they may have in mind a number of other cases). Yet it is not at
all clear that Louw and Nida’s evidence proves their claim – surely Matt. 14:35 does not provide sufficient
evidence, nor does the only other verse they cite in support, Rom. 4:8, for that is a quotation from Ps. 32:2,
a psalm in which David is speaking in the first instance about himself. That a man can be a representative
of a general truth appears from Psalm 1 and Psalm 32:2. But, as we have seen in discussing îsh and geber
(“man”), this observation does not eliminate the existence of a male semantic component in the
representative, the single person who embodies the general truth." (pages 305-306)
There is nothing in what Grudem and Poythress say here, that actually is a proper response to what Louw and Nida say in their lexicon, that "anēr has the meaning “person, human being, individual”". There is nothing in the Greek of Psalm 32:2, from where Paul is quoting, that dispoves what Louw and Nida say, nor prove the argument of Grudem and Poythress. I will add another verse from the LXX OT to show the weakness in what Grudem and Poythress are saying.
In Proverbs 6:12, it says, "A naughty person, a wicked man, walketh with a froward mouth" (KJV), for which the Greek is, "Ἀνὴρ ἄφρων καὶ παράνομος πορεύεται ὁδοὺς οὐκ ἀγαθάς", which literally is, "a foolish man and a lawbreaker shall go by ways not good".
This is a very interesting verse, which, for reasons of their bias in their one-sided arguments, Grudem and Poythress, don't include in their book, even though they do quote from elsewhere in Proverbs. Not only is "Ἀνὴρ" used here, which the KJV has rightly translated as "person" (as do most English versions); but, we also have the Greek adjactive, "παράνομος" (lawbreaker), in the nominative, singular, and either male of female, as it is in the masculine or feminine. Here is very clear evidence from Scripture, not ones bias, that proves beyond any doubt, and so rendered in almost every English version, where "Ἀνὴρ" is used, that it not exculsively "male". So, regardless of what people like Grudem and Poythress are arguing to push their "theology", the fact of usage as shown from the Bible itself, disproves their theory. I can give many more examples, but time prevents me.
I will give just one more example on gender use which is important. In 1 Corinthians 13:11, it says, "When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things". Here Paul uses the Greek adjective "νηπιος", 4 times, which is in the masculine gender. We also have "ανηρ" used once, where it is rendered "man", and "νηπιου" (childish), once, which is also in the masculine. Is Paul here specifically speaking of only himself, or of all believers? The use of the verb "βλεπομεν" in the next verse, which is in the plural, "we see", shows that Paul was not only speaking of himself, but as being true of all believers, which the entire chapter is addressing. Can anyone in all honesty really say, that the use of "νηπιος", here refers to "boys" only, and does not also include "girls"? Or, that "ανηρ" does not also include "women"? Scripture should be our guide in what we believe, even though it may go against our personal "theology".