NIV: correctly handles the word
NASB: accurately handling the word
NLT: correctly explains the word
NET Bible marginal note: "correctly handling" or "imparting it without deviation"
NAB: imparting the word... without deviation
The Message: laying out the truth plain and simple
Translations vary because orthotomeo is a metaphorical word referring to cutting straight. Is the emphasis on accurate workmanship? (NIV, NASB, most others) or on straight cutting, meaning without deviating to irrelevant teaching? (NAB, The Message).
Here are two reasons why I am starting to favor the sense of "without deviation."
1) Orthotomeo is used in LXX Prov 3:6 and 11:5 to refer to cutting a straight path - a path that does not meander. The word is not used elsewhere in the NT or LXX.
2) The context of 2 Tim 2:15 includes both warning against incorrect teaching and against pointless teaching. However, one of Paul's key warnings in the entire passage is against pointless speculation: "warn them not to argue about words" "avoid worldly and empty chatter" "refuse foolish and ignorant speculations".
If that is how Paul is using the metaphor, then his point is that teaching in the church needs to stick to the big important ideas and not get distracted into speculation, pointless debate, or error.
The picture: a fresco of Paul from a tomb believed by some to hold his actual remains. It is the oldest painting of Paul, and the sarcophagus contains bone fragments from the first or second century.