Sometimes when I take a 滴滴打车 taxi to the university campus, the driver asks me if I'm a student, and I reply something along the lines of:
I'm a teacher
Wǒ shì lǎoshī
As far as I can tell, this is grammatically correct. However, more than once, the driver replied:
You're a teacher
Nǐ dāng lǎoshī
It feels almost like they're correcting me, but I don't really understand why. It's possible 我是老师 sounds more along the lines of what a child might say as it's very simple. (It's also possible I simply misheard them.)
Question: What's the difference between 我是老师 or 我当老师?
Among the zillions of meanings of 当, one is "to act as", so maybe 我当老师 has a meaning closer to "I perform the role of a teacher". But I still see no concrete reason that 我是老师 is wrong or inferior.