Why did David Hilbert and Wilhelm Ackermann distinguish first-order logic from higher-order logic?

David Hilbert and Wilhelm Ackermann distinguished first-order logic from higher-order logic to clarify the scope of quantification within formal systems.1

In earlier logical frameworks, such as those developed by Gottlob Frege and the authors of Principia Mathematica, quantifiers were permitted to range over "higher-order" entities, including sets of individuals, properties of properties, and relations of relations. Hilbert and his associates sought to isolate systems that restricted quantification solely to individuals—the basic objects within a "universe of discourse"—thereby establishing what is now known as first-order predicate logic or the lower predicate calculus.1

This separation was formally expounded in their 1928 work, Grundzüge der Theoretischen Logik ("Basic Elements of Theoretical Logic"). By distinguishing these systems, they helped define the boundaries of formal logic, facilitating the development of proof theory and the rigorous study of the syntactic properties of logical languages.12