Every single sentence of the Bible has a meaning that must be understood and applies to Christians today in one or more ways. This includes every sentence in 1 Corinthians 11. In 1 Cor 11.2-16 Paul teaches that the Father is the authority of the Son, and that husbands are the authority of wives, and that women should cover their heads in the worship service.
In 21st century America, specifically, Hawaii (where I live), I still believe the Father is the authority over the Son and that husbands are the authority of wives. But I do not believe women should cover their heads in worship. I think they are free to do it if they want, but I do not believe they are required. Why? Am I simply picking and choosing?
Here is what I think is happening in that text: Paul is giving a specific application of Scriptural principles to the church in Corinth in AD 60(ish). We all understand this. I would tell any teacher at our church that they need to figure out what the universal principle in a passage is, and then, find possible applications for our current culture/place/time. We simply have an inspired example of that. If we believe that it is right to find relevant applications for our people today, wouldn’t it make sense that we would see examples in the Bible of this?
Where else do we see this? I think you see it in the same book of 1 Corinthians when Paul talks about food sacrificed to idols. Refraining from food sacrificed to idols is the specific application of a principle about loving those with weak consciences. Refraining from food is not the universal principle!
I think you also see applications being mentioned in things like holy kisses. I also was struck by another example today in Romans 13. Paul says all Christians must submit to governing authorities. A specific application he comes up with in Romans 13.6 is paying taxes. Universal principle=submission. Specific application=pay taxes. Those who live in the U.S. might feel like paying taxes is a universal principle that must always be obeyed. But what if you lived in Qatar or the Cayman Islands, where individual taxes are very different, if even non-existent (from my limited understanding). Might Christians there be having the same conversation we are having about head coverings? “How come you apply 1 Tim 2 (women cannot teach) but you don’t apply taxes? I know our government doesn’t require us to pay taxes but Paul says ‘for this reason you pay taxes’!” Getting the point?
I believe I am the one with the consistent hermeneutic (philosophy of interpretation). We must read, think, meditate, pray hard and pore over every text to really understand what is happening. If you do these things, it might make perfect sense why you could walk into a Kailua Baptist Church service and find men leading the church while women sing and pray and even prophesy (read Scripture?) with all kinds of different hairstyles.