Commenter Carrierwave writes:

The term “false brethren” is found TWICE in the KJV and identical Greek terms are used in each case. Once in Galatians 2:4 and in once in 2Cor.11:26. “ψευδάδελφος” In the Greek it is ONE WORD comprised of ‘compound words’ (two Greek terms) in English it is translated as “two words”. The first Greek word is “psuedo”; in the Greek this means a “pretender”, “erroneous”, “spurious”, “fake”. The second word “adelphos” translated “brother”. It’s root “delphos”– Greek meaning “the womb” denoting “a birth”. Brothers in Christ are those who have been “born again” “birthed” by the same agent: the Holy Spirit. A “false brethren” is one who is a “pretender”, “fake,” “spurious” brother.in Christ. It can only mean an “unsaved” person pretending to be a saved person.

This is a good argument about the term “false brethren”, although I do not think it is way in which Paul uses the term “false brethren”. Strong’s dictionary lists an alternative meaning “pretended associate”. Brother, in many cultures and counties, often means close companion. As such, when the Greeks used the word they probably meant what Americans understand as “backstabbers”. There is nothing to point to Paul not using the word in this sense, and this interpretation works very well in the surrounding context of the verse:

Gal 2:4 And that because of false brethren unawares brought in, who came in privily to spy out our liberty which we have in Christ Jesus, that they might bring us into bondage:

Paul talks about “spies” and being “secret” and being “stealth” (unawares). This is all backstabbing terminology. It seems like Paul is saying that these people came in, pretended to be nice to Paul and the Gentiles, and then subtly began teaching the law. This fits the context of Galatians well.