We say 'at noon' because noon is precise time on the clock. Noon is 12 o' clock. We say 'at 12 o'clock'', so we say 'at noon'. It's a time.

Morning, afternoon and evening are longer periods, so we use 'in'.  You can also say 'in the night'.

I think what Shirley is referring to are phrases such as:

"Meet me in the morning."

"Meet me in the afternoon."

While these two sentences are quite natural, a native English speaker would never say:

"Meet me in the night."  Instead, we'd say either:

"Meet me at night." or

"Meet me in the evening."  

I think the reason for this is because "night" isn't really the equivalent of "morning" or "afternoon"; it is the equivalent of "day".  And that is why you will not hear us say:

"Meet me in the day."

So, my point is:

night = day

morning = afternoon = evening

We can say "in the night." 

The English translation of the Bible uses the phrase "like a thief in the night."

A stock phrase for a brief encounter is "like ships that pass in the night."

In <em>Jane Eyre</em> Charlotte Bronte wrote "but you may call me if you want anything in the night."

In <em>Peter Pan</em> J. M. Barrie wrote "She explained in quite a matter-of-fact way that she thought Peter sometimes came to the nursery in the night..."

In <em>The Call of the Wild</em> Jack London wrote "All day they swung up and down the main street in long teams, and in the night their jingling bells still went by..."

We can say 'in the night'. For example you could say I woke up in the night. i saw a full moon in the night sky. You would always say at noon though (when talking about 12 o'clock)