1 Corinthians 10:29 (ESV)

29 I do not mean your conscience, but his. For why should my liberty be determined by someone else’s conscience?

In 1 Corinthians 10:29–30 Paul is anticipating possible objections from the Corinthians. Perhaps they have already voiced these objections in their letter to him. 

The objections are centred on Christian liberty in matters of food and drink. One can imagine a Corinthian believer arguing, I know in my own conscience that an idol is nothing. Why then should I, who know the truth, let myself be bound by the false beliefs of another?

Paul’s response to this objection is that the matter of sacrificial meat is not a matter of the believer’s conscience or of his liberty. Neither a believer’s liberty nor his knowledge of the truth is affected by the decision to abstain from sacrificial meat. It is for the sake of the unbeliever’s conscience that the believer must abstain. It is a limitation that the believer must willingly take on himself, for the sake of his neighbour (1 Corinthians 10:23–24).