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The idea of a priori knowledge is not that it's intuitive, but that it is not dependent on experience for it to be conceivable.
If I am understanding your statement here correctly, you are saying that a priori knowledge hinges on the idea that concepts can be acquired independently of experience. If that is what you are saying, then you would be incorrect. Very few philosophers who accept the idea of a priori knowledge—or more appropriately: a priori justification—think that human-beings ever acquire concepts innately or that they can otherwise conceive of them independently of experience. A proposition is knowable a priori if it is justifiable by appeal to pure reason or thought alone. Conversely, a proposition is knowable a posteriori if it is justifiable in virtue of experience; where any relevant, constitutive notion of experience would have as its meaning (a) some causally conditioned response to particular, contingent features of the world, and (b) doxastic states that have as their content information concerning such contingent features of the actual world as contrasted with other possible worlds.