Just talk to her about her insecurities and reassure her. Tell her that her request is too far, but you are willing to set boundaries so she will feel better.

Boundaries for her comfort are your choice and are not forced.

She can't stop you from having a female dance partner because that may not be your choice. But

You can tell her you will inform any woman you dance with that you are in a committed relationship.

Tell her that you will make the choice not to interact with women from the class outside the class.

You can also see if their are classes that are men only.

You can see if she is willing to be there because it's something you want to do, but she does not have to partake in the class.

Present options to her and tell her that your hobby isn't her choice but that you are willing to try and make things more comfortable for her.

If she is unwilling to work with you, her insecurities should be discussed with a therapist because they are interfering with her and her partners life.

Edit: This is all a moot point if she enjoys herself anyway.

I get that, but while her insecurities, opinions, and feelings should be considered, they do not give her the right to veto your hobbies.

She does not get to decide if you continue.

If she doesn't like it, that's fine. She doesn't want to do it, that's also fine. It is absolutely unfair and uncalled for that she says you're not allowed if she doesn't like it.

It's not an argument. It should be precedent that you're allowed to have hobbies that your wife does not share. Draw the line and hold it.

Ooooh, that's pretty interesting.