Question

What might keep a state from accepting a categorical grant in aid

Answer 1

Because they don't want to have to spend the money on specific things, they might want a block grant where they have more freedom with the money

Answer 2

Categorical grants are the main source of federal aid used for one specific purpose with strings attached. Block grants are given to states or communities and they decide how to spend the money. States prefer block grants because there are less strings attached and the money can be used for a broader purpose.