In Gal 3:10–4:7 Paul gives two reasons why works will not justify. One the one hand, he says that justification by works would change the terms of God’s covenant with Abraham. And, Paul adds, one simply isn’t allowed to do that sort of thing with an established covenant (see Gal 3:15–18). On the other hand, he says—or, at the very least, implies—that justification by works is impossible, since one would have to perfectly obey the law in its entirety to be justified (see Gal 3:10). Some think this second point misrepresents Judaism. After all, Paul’s insistence on perfect obedience fails to take on board the law’s own provision for imperfection: the sacrificial system. Has Paul (deliberately?) misrepresented Judaism or did Judaism, as Paul implies, actually require perfect obedience from those who wanted to live (Gal 3:12)? Tom Schreiner nicely slices the onion, noting that “[p]erfect obedience was not required under the Sinai covenant, for the law provided via sacrifices for those who transgressed. In Paul’s view, however (see Gal 3:15–4:7), the Sinai covenant was no longer in force. Therefore, those who observe circumcision and the law to obtain justification (Gal 5:2–4) are turning the clock backwards in salvation history” (Galatians, 213, emphasis added; cf. also n. 65), and are doing so without the benefit of the now-fulfilled sacrificial system. Thus, to borrow E. P. Sanders’ famous (and reductionistic) line, “This is what Paul finds wrong in Judaism: it is not Christianity.”
Note: For Schreiner’s resolution to the tension his solution creates with Paul’s first observation noted above (i.e., inheritance not through obedience but promise), see his comments on pp. 231–33, where he distinguishes between the promises (inheritance) of the Mosaic covenant (see, e.g., “land,” 233) and of the Abrahamic covenant (i.e., “final inheritance,” 231; salvation, 233). One came through obedience; the other through promise (233).