The Buddha thaught for his whole life after gaining enlightenemnt.
He could have simply vanished if He was only motivated by arhatship.
He did not vanish, he stayed and taught extensively.
Why did the Budddha await to be asked 3 times before he taught?
Not for any other reason than to ensure the proper mindset for the students.
How? This is how:
I ask one time, and maybe I hope the answer will be no, but I ask, because it looks good on me.
I ask again, this time perhaps with a better motivation and I am told no, will I be upset? Possibly
I ask a third time, and there are pretty good chances that on the 3rd time my motivation is much more sincere.
If I want to look good, if I am looking for praises, if I am not sincere, my mind is not in the best shape to listen to Dharma.
What if I listen and then do the opposite, what kind of karma is that?
The request for teaching is done 3 times, not as a matter of proticol (even though...) or because the Teacher needs to be reminded of bodhicitta (
). It is so that the listeners have a better mindset to receive the holy Dharma.
A Buddha is a bodhisattva.
A bodhisattava is an arhat.
And an arhat is an arhat.