No one else has ever said what I think from what I have read, and even my wife disagrees with me. But this is how I see it.
There are a few things to consider first.
The early believers did not “go to church” as understood today. They met in homes. The Jewish believers met in synagogues at first, but were kicked out by Jews who rejected Christ. Greek believers, of which Corinth was comprised, never met in the pagan temples, but in homes. Jewish believers in Jerusalem met in the Temple until cast out, but also met in homes to break bread together (Acts 2:46). Lydia had invited Paul & company into her home (Acts 16:15), which was a common practice which is why the Didache gave practical guidelines for entertaining traveling evangelists and apostles. In fact, church as we know developed around the 3rd century AD when Greek orators became Christians and saw a way to make a living preaching and teaching. Paul, of course, did the same thing, as seen in Acts 20, but it was not necessarily a weekly meeting for him. The point is this: the Corinthians were meeting and eating in homes, which was an interactive gathering of all the believers instead of just one man preaching or teaching.
The other consideration is the context surrounding chapter 11. What were the main points Paul was addressing? A short survey of the chapters will give context to the head covering issue, which really seems out of place and a non sequitur passage.
The Corinthians were still carnal and natural in their thinking, in need of really renewing their minds. They operated in the spiritual gifts, but lacked spiritual maturity. A common sight today with ministers who have had miraculous ministries only to fall in scandal of immorality.
Perhaps they thought they were mature because they functioned in the gifts. A trap common to many. Here is the survey.