> English has one case and if we try very hard we can squeeze something similar to a case - so let's say it has two

This isn't a correct way to describe English grammar. You can either say it has no cases or four cases with no inflections (because it definitely has subjects, objects, indirect objects, and possessives).

Presumably your native language doesn't inflect in the nominative or something like that and your English teacher once gave you your statement as a convenience fact, but the vast majority of native English speakers have never heard of grammatical case (ones who have, have typically studied inflected foreign languages). In Linguistics, it might be used to describe English and other uninflected languages (it depends).