Huh?
Half-dozen can be used for more objects than just eggs. A half-dozen ice cubes, a half-dozen stars, a half-dozen pigs, a half-dozen movies. There, just used half-dozen for other objects.
I think they mean, in the example, “half-dozen” is only for eggs..
Then, abstracted, any quantity of six.
First a number designation was object specific, then abstracted to the same quantity of any object. The number became abstracted from its specific context.
I think.
A better example might be Japanese where the words are modified for counting different things like people, time, the floors in a building, etc. English does this as well, but not nearly to the same extreme level of Japanese. For example, we use ‘primary’ and ‘first’ differently (where ‘primary’ is the first in a group or series while ‘first’ is a more general term).