Paring new partners every two weeks

I have a list of women and a list of men I need to pair separately as partners every two weeks. I want everyone to be paired up once before the rotation starts over. I want to be able to add or remove two people if necessary and have the rotation update. I have made an example but I am not set on this format of displaying pairs.
Other caveat - I need to be able to share the worksheet via Google sheets so there are some formulas which will not work, like TAKE. Big bummer. I have no idea even where to start so any help is appreciated!