Sometimes the words “major” and “big city” are just generic terms for cities that are well known by name and less to do with actual size of it's population or the cultures within.
Let's be honest only particular small segment of cities throughout America are very well-known by the general population with many cities throughout each state not being so known in general.
For example, NYC, DC, Atlanta, Chicago, Houston, Miami, Los Angeles, Boston, etc are cities that are just well-known “by heart” meaning anybody and everybody with a brain can name these cities right off top with ease.
I'd say every state on the map has a “major/big” city in terms of just being well-known right off the top of the dome.