Adam Clarke on Galatians 2:14

That they walked not uprightly - Ουκ ορθοποδουσι· They did not walk with a straight step - they did not maintain a firm footing.

According to the truth of the Gospel - According to that true doctrine, which states that Christ is the end of the law for justification to every one that believes; and that such are under no obligation to observe circumcision and the other peculiar rites and ceremonies of the law.

If thou, being a Jew, livest - This was a cutting reproof. He was a Jew, and had been circumstantially scrupulous in every thing relative to the law, and it required a miracle to convince him that the Gentiles were admitted, on their believing in Christ, to become members of the same Church, and fellow heirs of the hope of eternal life; and in consequence of this, he went in with the Gentiles and ate with them; i.e. associated with them as he would with Jews. But now, fearing them of the circumcision, he withdrew from this fellowship.

Why compellest thou the Gentiles - Thou didst once consider that they were not under such an obligation, and now thou actest as if thou didst consider the law in full force; but thou art convinced that the contrary is the case, yet actest differently! This is hypocrisy.