As Kant pointed out, the issue is in treating existence as a predicate. You cannot define something as extant; you must employ the scientific method to determine whether or not it is.
You could argue for the existence of anything otherwise. For example, we might conceive of a perfect cure for cancer. Obviously a perfect cure would be one that exists, since a cure that exists is better than one that does not. Therefore there exists a cure for cancer.
Again, the problem lies in defining something as perfect, because the assumption that it exists is embedded in such a definition.