A couple of more points. One is, assuming that faith is an action of the mind, like hope or love, then if we say something like "God gives faith to everyone" or "God gives hope to everyone" or "God gives love to everyone", what this means is that anyone has the ability to love, or hope, or "faith" (pretending that "faith" can be used as a very, like the other words hope and love, and like the Greek). So our disagreement here is more semantics than anything else.
Where the real disagreement lies is with the idea that a person can be reconciled, or justified by faith, apart from his will. This is something Calvinists assert (although the framework is quite different than yours). Armenians have always, in contrast to Calvinists, asserted the importance of the will in being reconciled or justified by faith.