In English, why do we say "in the morning" and "at noon"?

There is a really simple and logical answer to your question. I hope as a teacher i can give you the right information.

People are wanting to learn the English language. You do not help them by giving out wrong information.

‘At’ is a preposition to do with location. It can be a location in space or time.
at = means the action takes place for the period of the time stated.

It can be at a time as referenced by a clock (9pm) or a period of time (night).
In is a preposition to do with containment. We use it with time to indicate an action that happens within a time period.

In other words:
‘At night’ IS the time period something happens
‘In the night’ CONTAINS the time period that something happens.