Many languages distinguish between inclusive and exclusive first-person plural pronouns (“we”). (Click or tap here to see more details)
The inclusive “we” specifically includes the addressee (“you and I and possibly others”), while the exclusive “we” specifically excludes the addressee (“he/she/they and I, but not you”). This grammatical distinction is called “clusivity.” While Semitic languages such as Hebrew or most Indo-European languages such as Greek or English do not make that distinction, translators of languages with that distinction have to make a choice every time they encounter “we” or a form thereof (in English: “we,” “our,” or “us”).
“In Gal. 2:14 Paul quotes himself as speaking to Peter. If the quotation continues into v. 15, then the ‘We ourselves, who are Jews by birth’ [in English translation] would be translated as inclusive. More likely, however, the quotation ends with v. 14, the focus of attention then shifting to the Galatians, and so it would be exclusive we.”
Source: Velma B. Pickett in The Bible Translator 1964, p. 88f.
Nida (p. 205) also speaks of the problem of this specific verse:
“In Galatians 2:15 there is a troublesome passage for which the selection of an inclusive or exclusive form is highly debatable. The preceding sentence is obviously a part of direct discourse; but what are we to understand by the words “we ourselves, who are Jews by birth and not Gentile sinners”? Is Paul here continuing to represent what he said in Antioch in opposition to Peter, or is he merely arguing a general position with the Galatian church audience to whom he is writing? If one assumes that Paul is still addressing the assembly in Antioch, and Peter in particular, then the inclusive form is required; but if the words are directed to the church in Galatia, obviously one should employ the exclusive. Scholars are by no means agreed on this point, for the Greek text itself is obscure. Apparently there is a gradual shift from the specific situation which involved Peter to a general statement of the gospel as it is related to the Galatian church. The translator who is rendering this passage into a language with an inclusive-exclusive distinction cannot, however, retain this obscurity. He must specify clearly by the very forms he uses whether or not this sentence is to be regarded as a part of the direct discourse.”