Avrom, when you quoted my comment you left off the last part. That part answers your question. (Q – Shelo asani goy I can understand as Jewish pride, but why sing shelo asani isha as a song? A – the motivation [for singing would be the same motivation as] when saying the brocho itself and appreciating the reason Chazal instituted it.)
Chabadshlucha, I also asked about it being sung at a male-only event. (I gave some examples.) Based on your comment it appears you’d see that the same as singing shelo asani goy at a Jewish-only event.