The gift of faith

1. Freewill theists say faith is the empty hand that grasps the offer of salvation. Faith is not a product of saving grace; rather, saving grace is the result of faith. 

Let's compare that to Eph 2:8. Here's what one commentator and Greek scholar says:

In Greek, events as a whole are treated as neuter singular things with neuter articles, (e.g., to pisteuein, "believing"), neuter relative pronouns (e.g., Eph 5:5), or neuter demonstrative pronouns, as in v8b (also, for example, 6:1; 1 Cor 6:6,8; Phil 1:22,28; Col 3:20; 1 Thes 5:18; 1 Tim 2:1-3). Hence, the antecedent of touto is the whole event: "being saved by grace through faith". One implication of this proper understanding of touto is that all the components of the event are also referenced as originating not from human capacity or exertion but as God's gift. This means that even the believer's act of believing comes from God, as is said more explicitly by Paul elsewhere: "For it has been granted to you that for the sake of Christ you should not only believe in him…" (Phil 1:29). This is part of the evidence of Protestantism's historic position that salvation is sola gratia and sola fide). Humans contribute nothing of their own to this salvation, since even believing (which the elect are indeed enabled to do) is a divine gift (cf. Rom 3:24-25). In the context of Eph 2:8, the key to this is what Paul had been driving home so forcefully up until now: Before God's gracious intervention, believers were hopelessly dead, with their wills imprisoned by nature in acts that led only to transgression and sin (2:1-5a,12). S. M. Baugh, Ephesians (Lexham Press, 2016), 160-61.

So the gift in the second clause refers, via touto, to "For by grace you have been saved through faith." So God's gift is salvation by grace through faith". Faith is included in the gift. Faith isn't something by which Christians receive the gift, but a part of God's gracious saving endowment. 

2. On a related note, freewill theists typically say that for something to be a gift, the recipient must be able to refuse it. Compare that to John Barclay's Paul and Gift (chap. 2), where he reviews different connotations of a "gift" or benefaction in antiquity. Take his category of "efficacy", where gift-giving is powerful, accomplishing its purpose–as when parents give the gift of life to their children or someone is rescued from death. In those situations, the recipient is passive and helpless. 

By the same token, he cites a passage from Philo stressing the efficacy of grace to the point of human passivity and inactivity, attributing all to the sovereignty of God.

Moreover, in patronage system of the Roman Empire, a powerful benefactor isn't offering a gift. Rather, he confers a gift. 

And the asymmetrical dynamic between social superiors and social inferiors in the ancient world is far more analogous to the relationship between God and creatures than birthday gifts and Christmas presents between peers.

The efficacious concept of gift-giving is incompatible with grace in freewill theism, which is resistible and therefore inefficacious.