Mixed Doubles Schedule?

[Midpack]

I’ve been putting together a mixed doubles schedule every week, sometimes 4 guys/4 girls, usually 6/6. What the admin wants:

1. Never put two guys together.
2. Have each girl play against all other girls.
3. Have each girl play with a different guy each game.
4. No repeats of girls or guys against if possible.
5. We usually play 5-6 games.

Making that work for 4/4 is easy, but for the life of me I can’t make 6/6 work without violating 4 WRT guys above.

Here’s a couples mixed doubles guru who says it’s mathematically impossible/no balanced schedule exists, but I don’t understand why? https://www.devenezia.com/round-robin/forum/index.php?topic=769.0

Any of you math wizards know, or have a suitable schedule I can copy?