Both my Tai Chi teachers eschew the title of “Master”, and prefer to be called by their first names. As I’ve had it explained to me, even the true masters feel like they need a couple extra lifetimes to completely master Tai Chi. This is what my teachers compare themselves to, so I suspect they feel it erroneous to use the same title, even though they’ve been teaching for decades.
I find it very awkward. In Chinese, the word “Master” or “Sifu” implies a teacher, not necessarily a level of skill.
When I was young, I called my cousin by his Chinese name, because I thought it was insulting to address him by his relational title of biu dai for “maternal younger male cousin” (or “mother’s siblings’ son who is younger than me”). I thought the “dai” part referred to someone as “under”, the way “junior” could be used pejoratively in English. The thing I didn’t understand was that it was appropriate, perhaps even more appropriate than addressing him by name. I’ve since become privy to the complex rules of Chinese names and titles, especially relational family ones.
People continue this tradition though, and even as parents, they’ll address their elders the same way. It’s a way of recognizing and respecting the roles in the family. Even though my Tai Chi teacher is Occidental, I feel compelled to address my teacher as “Master”, instead of “Mike”.
And it’s hard habit for me to break.

I thought dai meant large? or is that another pronunciation?
Sifu, even though it means teacher, calls up the ancient automatic status one received as a scholar, which was more like we would revere someone like Steven Hawking or something. It is highly honorific, I can see why they felt awkward. Although it is traditionally theirs to claim…I rather like Sifu better too.
And the family relational names! Holy smokes, I have to learn all of them in Korean really soon for my trip.…not to mention proper bowing technique…
You’re right, it’s another pronunciation. The “dai” sound can be both “big” and “under”.
Sifu in Chinese simply means teacher. It’s not highly honorific, just respectful. A Sifu can be a cook, a calligrapher, or even a carpenter. It’s also used casually, like the American “boss” or British “guv’nor”. It was Westerners coming back from World War II, with grandiose stories of martial feats, who gave the mysticism of Sifu it’s meaning. To the Chinese it’s always remained the same; the title of someone who passes knowledge on to others.