1. Necessarily, if X and Y possess all of the same attributes, then X and Y are identical. (Premise, Leibniz's Law)
2. Necessarily, if some not-real A possesses all of the same attributes as some real B, then A and B are identical. (From 1)
3. A not-real A cannot possess all of the same attributes as B. (Premise)
4. Therefore, A and B are distinct. (From 2 and 3)
(1) states the relatively uncontroversial axiom of logic known as Leibniz's Law. Now, if existence is not a predicate, then (2) requires that A and B possess all of the same attributes. The problem is that A does not exist, whereas B does exist. The only difference between the two would be existence, but since existence does not exist, it follows that A and B are distinct by nothing. However, to be distinct by nothing is to be identical, which entails that A and B are actually identical and not distinct. You can all decide for yourselves if that's a rational position.
If you're anything like me, though, you'll affirm (3) (and hence (4) as well) and reject Kant's Assertion.