In Chinese, 名 (famous) and 明 (enlightened or knowledgeable) sound the same. We prefer to seek the knowledgeable teacher to learn. In this case, knowledgeable refers to the knowledge of imparting knowledge. Not that famous teachers are bad in that, but sometimes with fame and commericalization, proper knowledge transfer becomes secondary.

Good taiji teachers should have good knowledge of taiji. They should not talk in terms of yi or qi too much. They should understand each student are different in their rate of learning. taiji should be easy to learn and pick up. Mastering it is another matter.