For itineraries that include international flights (except Canada), checking a first and second bag will continue to be free, United said. The cost to check more than two bags or items that are overweight or require special handling varies by destination.

Please help me understand why 'bag' is not plural.
the/a first bag
the/a second bag
each one is a bag in its own right.
Ten bags were checked in. Only the second bag checked in was opened by Security
Sorry, Optilang. I still don't get it.
a first and second means there are two bags. To me, it's the same as saying a first(bag) and a second (bag), therefore, two bags in total.
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a first (bag) and a second (bag)
So only 1 first bag and only 1 second bag = 2 bags in total. BUT each bag is only ONE
I chose an orange, then I chose a second and third orange. The first orange was ripe, the second orange was bitter, and the third orange was sweet. Total = 3 oranges.
"So only 1 first bag and only 1 second bag = 2 bags in total. BUT each bag is only ONE "

Myunderstanding of AND is not each but BOTH. I would correct the bolded words as "BOTH bags ARE two"

Another example
I bought an orange bag and a red bag. THEY (not IT) are spacious.
New2grammara first and second bag
a first (bag) and (a) second bag. You can't have a with a plural so a ... bags is out of the question.
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Good point, CJ. But what does it mean? Below are some similar constructions that I'm familiar with

a point
a first point
a second point
the point
the first point
the second point
The first and second pointS

I've never heard of "a first and second point", not to mention the meaning of it.

On the other hand, I have no problem with a blue and red shirt. I can imagine two colors on a shirt.But I can't image "first and second" describing a point. They can't be mixed like colors.
How about:
I bought a shirt yesterday morning, and I bought a second shirt in the afternoon.