In Tai Chi, Qigong and Chinese martial arts who your teacher is has significance.  It indicates the 'lineage', a chain of knowledge of which you are a part.  If you are a teacher this 'chain' extends to your students.  They too are a part of this long tradition of knowledge.  

The diagram below was created by Dr Shen's son, Shen ZhengYu, and shows the main traditions of Tai Chi and Chinese and Tibetan Buddhism and the teachers/lineages that formed Dr Shen.