Proof texting, in apologetics, is when someone who is attempting to make an argument from the Scriptures resorts to citing isolated verses out of context to make their point.
For example, someone may say, based on Matthew 23:9, “Call no man father,” that Catholics should not call priests Father. But if you look at the text in context (look at the entire passage in which this verse appears, Matthew 23:1-12) you will see the point of Jesus’ remark is not to forbid calling anyone father (in which case you’d be at odds on what to call your male parent), but is in fact an exhortation on avoiding the pursuit of titles and to rather pursue humility.
Proof texting works both ways in that, if a catholic apologist himself stoops to this tactic, the argument turns into one of “I have more verses that prove my point than you do.” This is known as “verse slinging” and tends to accomplish very little.