It is difficult to explain unless you owned one and compared them.
The 13" MacBook Air is almost 50% (!!) heavier in weight than the 12" MacBook. That is -a-lot- of additional weight - for a laptop.
And it is 1 inch wider and 1/2 inch deeper, which means it does not fit in the same bags or spaces.
Or to put it differently:
For the 13" MacBook Air you need a dedicated attache or laptop bag, and you are feeling that you carry a "real" laptop bag around all day, and your shoulder will eventually get hurting and stiff from you carrying it all day. At least mine did.
The 12" MacBook is lighter and thinner than a 11" iPad with case, and a lot so with the magic keyboard case!
It can fit into almost any bag - does not need to be a dedicated laptop bag. I carry it in a tiny sling bag.
And weighing so little, I often even forget it is in my bag or not. It doesn't hurt my shoulder if I carry it all day.
At home, because it is so small, it fits on any ledge or tiny table, it can easily be carried with two fingers, makes no noise (has no fan), and is overall a lot more versatile than any iPad Pro ever can be.
The 12" MacBook to me is total freedom. You don't feel the weight in your bag, you can use really small bags - no one would think there's a laptop in it - it fits onto any tiny space and seat tray, often even with room for a coffee next to it.
Why would I want a big and heavy 13" MacBook Air?!?