Wikipedia
Prooftexting (sometimes "proof-texting" or "proof texting") is the practice of using isolated, out-of-context quotations from a document to establish a proposition in eisegesis. Such quotes may not accurately reflect the original intent of the author, and a document quoted in such a manner, when read as a whole, may not support the proposition for which it was cited. The term has currency primarily in theological and exegetical circles.
This is to be distinguished from quotations from a source deemed a hostile witness, which inadvertently substantiate a point beneficial to the quoter in the course of its own narrative. Even when lifted out of context, those facts still stand.
Many Christian ministers and Christian teachers have used some version of the following humorous anecdote to demonstrate the dangers of prooftexting: "A man dissatisfied with his life decided to consult the Bible for guidance. Closing his eyes, he flipped the book open and pointed to a spot on the page. Opening his eyes, he read the verse under his finger. It read, 'Then Judas went away and hanged himself' (Matthew 27:5b). Finding these words unhelpful, the man randomly selected another verse. This one read, 'Jesus told him, "Go and do likewise."' (Luke 10:37b). In desperation, he tried one more time. The text he found was: 'What you are about to do, do quickly.'" (John 13:27)