That doesn't really sound right in my ears. Exchange is more natural. Barter is for tangible products. For example: He bartered 3 gallons of milk for 2 pounds of wool.

No problem! Good luck on your English studies!

Thank you so much Paari!

Bartering is used more with goods rather than services. Usually, when you deal with services you would use trade, because barter doesn't make as much sense when trying to fit it in the sentence. When dealing with services, you would usually use time to indicate the exchange of services.

When they mean services they mean things like promise you'll barter my freedom if Qatwali imprisons me on this peace mission. But in your situation, you're using language as the thing you're bartering(you can't literally trade languages). A better sentence would be "I like the fact that everyone on Italki can barter their time to teach their native language in exchange for help in their target language.