Ptolemy's World Map from Geographia, c. 150 c.e. (source: wikipedia)

Gerrit Cornelis Berkouwer (1903-1996) was a famous Dutch Reformed Theologian who worked within the same illustrious Dutch Calvinist tradition as Abraham Kuyper and Herman Bavinck. In G.C. Berkouwer's Studies in Dogmatics: Holy Scripture, is a famous argument against inerracy that I've quoted in toto below. G.C. Berkouwer's rejection of inerrancy may be summarized as:

From Studies in Dogmatics: Holy Scriptures:

The origin of the dispute is related to this question: in view of the truth and reliability of Holy Scripture, is it legitimate to believe that numerous conceptions occur in it that fit the world view of an earlier age and not that of a later age? Does not such a notion of a biblical world view call into question the authority of Scripture for all ages? A lively debate took place particularly in the Reformed churches in the Netherlands after the Synod of Assen, which dealt extensively with the direct application of the authority of Scripture. The conviction was defended at that time that, though the Bible does not offer a scientific world view, yet the cosmological presuppositions of the biblical authors clearly demonstrate a contemporaneous view of the structure of the world: for instance, the earth as flat, surrounded by oceans--a geocentric world view held by no one today. It was pointed out that the authority of Scripture is in no way diminished because an ancient world view occurs in it; for it was not the purpose of Scripture to offer revealing information on that level. Here again we encounter the problem of the relationship between the God-breathed character of Scripture and continuity. In these discussions we find different attributes of Holy Scripture, namely, its reliability, its infallibility, and its inerrancy.

Note: The setting of the "inerrancy" discussion is developed in detail by Warfield, op. cit., pp. 150f. He sees "inerrancy" as implied in reliability and then with regard to "all its parts and in all its elements, down to the least minutiae, in form of expression as well as in substance of teaching" (p. 150). Cf. "entire truthfulness" as "inerrancy" in verbal inspiration (which he does not see as dictation) through which Scripture is protected "from everything inconsistent with a divine authorship" (p. 173) and from whatever conflicts with "a divine book" (p. 151).

The fact that the Bible contains an "obsolete" world view, and thus an incorrect and erring world view, contradicts the God-breathed character of Scripture, according to this viewpoint, since each "error" is excluded by the God-breathed character of Scripture. In this view of inerrancy we meet a serious formalization of the concept of erring. The concept of error in the sense of incorrectness is obviously being used on the same level as the concept of erring in the sense of sin and deception. The distinction is left rather vague. As a consequence of this, limited historical perception within a certain cultural and scientific situation is, without further stipulation, put on a par with erring in the sense of lying, the opposite of truth. If erring is formalized in such a way, it cannot later be related to truth in the biblical sense, but it continues to function as a formal structure of exactness and correctness. Thus, we are quite far removed from the serious manner with which erring is dealt in Scripture. For there what is meant is not the result of a limited degree of knowledge, but it is a swerving from the truth and upsetting the faith (2 Tim 2:18). The testimony of the Spirit stands opposite that erring, and the confession of the God-breathed Scripture could not be maintained with that kind of deception in view. The supposition that limited human knowledge and time-boundedness of any kind would cause someone to err and that Holy Scripture would no longer be the lamp to our feet unless every time-bounded conception could be corrected, is a denial of the significance of historical development and of searching out as the "unhappy business that God has given to the sons of men to be busy with" (Eccl 1:13). It can be recognized that "inerrancy" was emphasized with the intention of warning against a mistrust of the testimony of God and of keeping the church from really erring. But the formalization of inerrancy virtually destroys this intention, because the relationship of the organic, God-breathed character to the organic unity and scope of the total testimony of Scripture is almost totally ignored. It creates numerous insoluble problems in the historical development, so that as a consequence in later years a compromise could no longer be avoided, and various solutions were proposed that made inerrancy a latent dogma without any real function. The problem of the God-breathed character of Scripture and continuity gained renewed interest in its connection with the authors' level of knowledge in a certain period (Ex 20:4; Ps 24:2; 2 Sam 22:8; Ps 136:6; Job 26:5; Ps 46:3; Ps 148:4). This does not mean a capitulation to science as an institution opposed to God's Word, with the additional conclusion that Scripture is unreliable and its witness untrustworthy. Rather, it means a greater degree of naturalness in speaking of Scripture, with a view to its nature and purpose. Corrections of various conceptions of the world--its composition and its place in the universe--are not at all needed then to guarentee the full and clear message of Scripture. Formal problems of correctness (inerrancy alongside infallibility) disintegrate with such a naturalness. This is illustrated in Jan Ridderbos' words: "Moreover Scripture bears the marks of the period and of the milieu in which it was written and it shares in part these marks with the culture of the entire Orient, a culture which in many ways was interrelated to that of Israel. This is true for writing, language, style, literary genre, ideas, conceptions, world view (cf. the three-decker unvierse in Ex 20:4)." [Geref. Schriftbeschouwing en Organische Opvatting (1926), pp. 25f] It is possible to be so natural, without a sense of crisis concerning the confession of Scripture, because there is no reason why "a certain time-related conception concerning the composition of the universe" has to be corrected. He who demands that all conceptions occurring in Scripture be precisely correct on the basis of the God-breathed character of Scripture starts with the presupposition that the voice of God can only then be reliable and that the biblical authors cannot be witnesses and instruments of the God-breathed Scripture when they use certain time-bounded conceptions in their writings. This notion of "inerrancy" can quickly  lead to the idea that the "correctness" of all these conceptions anticipates later scientific discovery: "What a marvelous book that anticipates this triumph of man's ingenuity some four thousand years or more." [E.g., Job 38:35. See B. Ramm, The Christian View of Science and Scripture (1963), pp. 162f.] This anticipation is being adduced then as a sign of the divinity of the Scripture. However strange they may sound, such ideas should not be ridiculed. The question is rather how such a theory of inspiration is being applied and how some are fascinated by a miraculous "correctness" that forever disregards every problem of time-relatedness. Even though one may hear through it all a note of serious motivation, the conclusion is valid that this earnestness cannot serve as yardstick for the doctrine of Scripture. In the end it will damage reverence for Scripture more than it will further it. Ramm wrote rightly (cf. Bavinck's opinion concerning the knowledge of the biblical authors) that the Holy Spirit "did not give the writers the secrets of modern science." [Ibid., p. 136] Various excessive examples (including even nuclear theories) are in his opinion "a misunderstanding of the nature of inspiration." They do not take into account that Scripture came to us "in terms of the culture in which the writers wrote." [Ibid., p. 96.] This does not imply a dualistic theory of inspiration. For this unmistakable emphasis, as well as the reflection about the nature of faith, corresponds with the intention of Scripture itself. It offers explicit and implicit evidence that is not a "gnostic" writing but the God-breathed Scripture oriented to the testimony of God's deeds, profitable for teaching, for reproof, for correction, and for training in righteousness (2 Tim 3:16). It is not that Scripture offers us no information but that the nature of this information is unique. It is governed by the purpose of God's revelation. The view of inspiration that forms the basis of the misunderstanding of this purpose considers "inerrancy" essential as a parallel characteristic of reliability; that is a flight of fancy away from this purpose. Berkouwer, Gerit C. Holy Scripture. Trans. Jack Bartlett Rogers. Grand Rapids: W.B. Eerdmans Pub., 1975. 181-84. Print. Studies in Dogmatics.