(This post has been edited to sound less accusatory as several users pointed out)
I am American and my native language is English.
You can't make a private community within Math Stack Exchange, and I'm sensing that the community is against including other languages in a private forum setting. Using another language can make it harder for many people to access your posts, in addition, your request for a private forum makes it seem like you'd want to operate it within the rules of your class. However, all posts on this site have to made within the rules of this site, not your class. So sadly, it seems you'll have to find another site, or you'll have to be accepting of the public nature of this site.
However, having said that, I find it odd that in the 5+ years this site has been active, we still don't have sites for people who speak other languages. I find it annoying that such a site can't be created, as pointed out in comments above, because sites can only be created in Area 51, and that site doesn't support other languages either.
I understand that English is the universal language of the sciences, and that we encourage people to communicate using it. But I hope that you'll be free to use other languages on this site. I hope the community isn't hostile to that reasonable request for accessibility.
I believe your next course of action is to go to Area 51 and ask for accommodation there as it looks like you'll unfortunately have to create a new site. Of course, you'd could always decide that having a public rather than private site would be best, in which case you might very well be able to use this site.