China has some reputable training centers. Their FTs are treated well in all repects. They
are deemed to be great teachers by their students because they enliven their kids by
playing games and acting the giddy goat

Simon may say, but Simon cannot write.

The 'their' in your second sentence varies in subject (training centers) to the 'they' and 'their' (FTs) in your third sentence.

"Their students" acts as the subject of the second sentence so "their kids" would actually refer to the students' kids.

If students 'deem' the FT to be a great teacher because the teacher acts "the giddy goat", how does that establish a training center as being reputable?

If giddy goat FTs make training centers reputable, then all Chinese training centers are reputable.