William Cunningham: Arminians and Romanists both deny the biblical doctrine of substitution and satisfaction by Christ

“Papists unite with Arminians in denying the necessity of a perfect righteousness, as the ground or basis of God’s act in accepting men’s persons, and giving them a right and title to heaven … As the Scriptures indicate that a perfect righteousness is necessary, as the ground or basis of our acceptance and admission to a right to life, as well as a full satisfaction as the ground or basis of our forgiveness or exemption from punishment, so they set before us such a perfect righteousness as available for us, and actually benefiting us, in the obedience which Christ, as our surety, rendered to all the requirements of the law.” (William Cunningham, "Historical Theology," vol. II, pp. 49, 51; quoted in a compilation by Lee Irons)

William Cunningham: Justification is not a legal fiction

“The righteousness of Christ, including the whole of His perfect and meritorious obedience to the law, as well as His suffering, was a great and infinitely important reality. It was intended to effect and secure the salvation of all those whom God had chosen in Christ before the foundation of the world. It is in due time, and in accordance with the arrangements which God in His infinite wisdom has laid down, bestowed upon each of them, through his union to Christ by faith, not in any mere fiction of law, but in actual deed; and being thus really, and not merely putatively or by a fiction, bestowed upon them, it is, of course, held or reckoned as theirs, and thus becomes the ground - the full and adequate ground - on which God further bestows upon them the forgiveness of their sins, and a right to the heavenly inheritance, and to all the privileges of sonship.” (Cunningham, Historical Theology, vol. II, pp. 55-56; quoted by Lee Irons)

William Cunningham: Arminians err fatally on the doctrine of the atonement

William Cunningham pinpoints the Arminian deviations from the biblical doctrine of Christ's atonement in substituting Himself to satisfy the requirements of the Law for His chosen people to reconcile them to God:

The Arminians, holding the universality of the atonement, and rejecting the doctrine of election, regard the death of Christ as equally fitted, and equally intended, to promote the spiritual welfare and eternal salvation of all men. ... Arminians teach that Christ, by his sufferings and death, impetrated or procured pardon and reconciliation for all men ... in substance, he removed legal obstacles, and opened a door for God to bestow pardon and reconciliation upon all who would accept. The reason why they do not receive is because they refuse the offer made to them. Contrast: WCOF -- “To all those for whom Christ hath purchased redemption, he doth certainly and effectually apply and communicate the same.” An impetration which may possibly not be followed by application ... which will leave many for whom it was undertaken and effected, to perish forever, unpardoned and unreconciled, -- does not correspond with, or come up to, the doctrines of substitution and satisfaction taught us in Scripture ... Reconciliation was purchased by Christ’s sacrifice of himself, and purchased for certain men. Remember: the nature of the atonement determines its extent. Those who hold to universal atonement, in a greater and lesser degree, have defective and erroneous views with respect to the substitution and satisfaction of Christ. (William Cunningham, Historical Theology)

William Cunningham: The Reformers agreed on faith alone, but faith is not meritorious

William Cunningham explains the loose sense in which we are justified by faith alone, not by any inherent righteousness within us:

The Reformers were unanimous and decided in maintaining the doctrine that faith alone justified; that men were justified by faith only; and this gave rise to a great deal of discussion between them and the Romanists … By this position that faith alone justifies, the Reformers meant in general that faith was the only thing in a man himself, to the exclusion of all personal righteousness, habitual or actual, of all other Christian graces, and of all good works, to which his forgiveness and acceptance with God are attributed or ascribed in Scripture … They did not teach that this faith which alone justified was ever alone, or unaccompanied with other graces; but, on the contrary, they maintain that, to adopt the words of our Confession, ‘it is ever accompanied with all other saving graces, and is no dead faith, but worketh by love’ [Larger Catechism, q. 153]. … Again, the Reformers did not ascribe to faith, in the matter of justification, any meritorious or inherent efficacy in producing the result, but regarded it simply as the instrument or hand by which a man apprehended or laid hold of, and appropriated to himself, the righteousness of Christ; and it was only in that very general and, strictly speaking, loose and improper sense, which was consistent with this view of its function and operation in the matter, that they called it, as Calvin does … the cause of justification. (William Cunningham, Historical Theology [vol. 2], p. 23; published by Still Waters Revival Books)