As Standard German doesn't distinguish between the simple and progressive aspects, a sentence such as "Wir lesen" can mean both "We read" and "We are reading".
That's not the case here, however. The German sentence "Wir haben Suppe" means only that soup is available, that we "own" it. It's the same meaning as in a sentence such as "We have a book".
The English sentence, "We are having soup", by contrast, means that we are eating or planning to eat soup. That's not what the German sentence means.
Not all languages are the same.
The difference between German and English is obvious, with them having a singular and plural second person (you), every noun starting with a capital letter and the different versions of "The". When said "We are having soup" is, at least to me, equivalent to "We are eating soup", but, as Katrherle said above, it isn't used as such in German.
"We're having soup" is immediate future, which is not at all the same as owning or eating soup. It would be equal to "we are going to have soup." The confusion is simply that no one in America has ever uttered the words "we have soup" unless a small child is crying for a can of soup in a store. It's a thought we've never had!