It could be that the way we are reading a text is influenced by years of Watchtower indoctrination or some other view we hold that we never put to the test. I know that for myself I decided to invest several years to critical philology and similar studies after leaving the Witnesses because I wanted to know how much of religion and the Bible I was still judging by holdovers from the Governing Body and how much was actually from the Bible itself. (Of course this may not at all have anything to do with your views and where you get them. )
While this is not an endorsement that what I am presenting is the final word on these texts, I did learn the following alternative possibilities.
Matthew 7.13—Rabbis like to show us two paths.
Jewish teachers commonly use the imagery of two paths or two possible ways to take their teaching and the result to us if we choose one path over another. Deuteronomy 30.15 has Moses setting paths of life and death before the nation of Israel. The first Psalm is a contrast between the way a righteous person takes compared with that of someone who ignores the teaching of Torah. The Sermon on the Mount ends with Jesus setting two ways people can respond to his teaching, either using it as a foundation for life or “building upon sand,” and the results of either decision. (Matthew 7.24-27) The text in Matthew 7.13 is using the same type of imagery, a parable or hyperbole type of speech employing a common rabbinical model: the narrow and difficult way that “few” find and the broad and wide one that gets found by “many.” Notice that “few” and “many” are the result of Jesus telling everyone who listens to (and now reads) his words to accept his invitation to do one over the other. It’s an open invitation, not a prophecy.
It should be of interest that Matthew 7.13 has this “two path” imagery in common with James 1.15.
James 1.15—More dual path stuff.
James is written in a peculiar proverbial style, like wisdom literature of the Old Testament. The text from James might also be employing identical patterns, and verse 12-15 seem part of a section discussing what happens to those who don’t follow God’s teaching. For instance, 12-13 gives the impression that anyone can withstand temptation since God is not the source of making a person’s life sinful. Verses 14-15 show the result if the person chooses to act independent of God.
This pattern is followed at first three times in chapter 1 of James, namely 5-8, then 9-11, and finally 12-13. It picks up for fourth time in 22-25. Why? James is talking about application of the “word,” as you mention, only he is speaking about the laws of God here. Note that the other verses in the first chapter are about asking God for guidance and how God will generously supply those who truly want it.
Of course 17 and 22 aren’t speaking about rain or Jesus. But I am sure you know that. Also, this is just one way scholars deal with these texts and not necessarily reflective of my own convictions. I can't speak for you, but I know I often blamed Scripture or religious people in general for my views of Scripture and "worldly" people that I learned years later didn't originate with them.
And I agree with Heaven, not being thrilled with the misogyny in Scripture.
Of course, the misogyny is not from Jewish culture or invented necessarily in Scripture, but reflective of Hellenistic or social mores and customs.
The texts is 1 Co 11.5-13 have to do with Gentile head covering issues, not those followed by the Jewish Church in Jerusalem. While it would not become a universal custom for Jewish men to wear kippah until after the Second Temple fell, it is widely held that the custom took root after the return from Babylon. The fact that priests at the Temple wore headcoverings in worship and many priests that served at the Temple became Christians shows that Paul had to be addressing something particular to the Gentile group.
For instance, the prophetess Anna, daughter of Phanuel, freely spoke and prophesied in the Temple. (Luke 2.36-38) This is contrary to Paul’s words of 1 Corinthians 14.34. Did Anna break Mosaic Law or is Paul referring to another law of submission that the Corinthians were aware of because women served in the capacity of synagogue leaders in the first century as well as civil leaders (Antiquities 13.405; see also
http://www.patheos.com/blogs/jesuscreed/2013/03/07/women-in-first-century-synagogues/).
Thus the misogyny is not from Mosaic Law but a reflection of some other law that would have been understood by non-Jews in the exhortation from Paul.
Paul’s instruction in these other verses are also in epistles written to Gentiles, and even his letter to Timothy is speaking about what Paul allows and does not allow in Gentile Churches. Paul’s words did not cover his views and practices for Acts 21.15-26 state that he and members of Jewish Churches still followed Jewish practice.