Greek subjects and verbs
The interesting thing is that ἐστιν can mean both "he is" and "she is." It can also mean "it is."
In other words, the Greek verb tells us something about its subject. In the case of ἐστιν, the verb tells us the subject is a "he," "she," or "it," and not a "they" or "you." (How does it do this? We will talk about that later.)
This is why a Greek speaker could just say ἐστιν διδάσκαλος μου, and the person hearing would understand that "He" or "She" "is my teacher."
But let's say you want to be clear. You want to say that "She" is your teacher. How would you do that?
You would use the specific word for "she."