From a response to an email:

Keeping the equations in balance is a good example: we’re taught we “must” keep them equal. I prefer to think of it like this:

If we have two things that are the same size (a = b), and we want to keep them the same size, then we have to do the same thing to both sides.

For example, if a = b, then

a + 3 = b + 3

If we only make a change on one side:

a + 3

then we know we’ve tipped the scales in favor of a, so we have

a + 3 > b

That’s a perfectly valid equation, by the way, but it’s not as helpful or precise as saying what something is equal to. (“This shoe will cost you $14.73” vs “This shoe will cost you something over $10.”).

I think that’s the unstated assumption, we want to keep things as specific as we can, because knowing what something is equal to is better than knowing what it’s greater than.