The student was trying to structure an interrupter. I am looking for a grammatical explanation to help her understand the error between the conjunction and the preposition. Beyond just explaining the meaning of each term ('even though' and 'with'), isn't the subject also needed before the interrupter begins?
On the other hand, big cities are excellent places for people who like diversity. These cities have a population of millions of people. People around the world come to big cities to find better job opportunities, or because they are looking for places with lots of fun. Even though, with many people going from one place to another, traffic on the streets will always be a problem in the big cities. Unlike from small towns, the social environment is more diverse.