一緒のチームになりたくないって英語でなんて言うの？

These are both standard ways to speaking and expressing desires. You can either us the possessive sense 'Asano-san's team' or say 'same team as Asano-san' using 'as' in the adjective form.

"I don't want to be on their team." This would be used when referencing to another person. It is straight to the point, but it could possibly come across as a little bit rude. "I would rather be on a separate team." This is a more polite way to tell someone that you would like to be put on different teams. "Could we please be on different teams?" This is my favourite way of saying this. It is the most polite option. When referring to someone else (the person you don't want to be on the same team as), you are asking whether it is ok if you are separate. Adding 'please' is also extra polite.

I don't want to be on the same team' means that you want to be on a different team to somebody. 'Can I please be put in a different team to him/her/them?' is a question asking whether you can be on a different team to somebody, adding 'please' to make it polite. 'I think it's better if I am on a different team to him/her/them.' is a suggestion that there may be an advantage to being on a different team to a certain person.

These are two different polite ways to express that you don't wish to be on someone's team. This will help to show that you don't want to without making anyone feel bad. I hope that this helps :)

If you would like to explain that you don't want to be on the same team/side as someone, you can do so in the following ways: "I don't wan't to be on the same team as him!" "I don't want to be on John's team!"

If you are doing an activity that involves teams and you don't like someone who is also participating and you hope you are on different sides, the strongest ways are to say "I hope i'm on a different team than ..." or "I really don't want to be on the same team as. ...".