There are numerous ways to try and entertain yourself on a plane - from reading, to podcasts, gaming, to chatting with your seatmate. But there are certain things that are generally frowned upon as they're not appropriate for enclosed spaces.
It's generally accepted that one of these activities is painting your nails. Not only would it be a difficult task to complete, especially if there was turbulence on the plane, but the smell would also undoubtedly fill the cabin, and cause several people discomfort.
Whilst some were horrified by the woman's "entitled" behaviour though, some saw no issue with the activity.