Why does one string sound sharp when I fret it?

A single sharp string narrows the problem down. Work through the likely causes in order.

1. Check your fretting pressure. Play the note lightly, then firmly. If the firm note is clearly sharper, ease off. Press just behind the fret with only enough pressure to stop buzz.
2. Check for sideways pull. Pushing the string across the fret bends it sharp, the same as a small bend.
3. Check the nut. If the 1st and 2nd frets are sharp but higher frets are fine, the string may sit too high in its nut slot. Lowering a slot is a technician's job.
4. Check intonation. Compare the 12th-fret harmonic to the fretted 12th. Adjust that string's saddle if they differ.
5. Check the string. An old, kinked or poorly seated string can behave differently from the others. Replace it.

The 3rd string on electric guitars gets this complaint often. It's sensitive to fretting pressure, and a plain 3rd is stiffer for its pitch than its neighbors. A wound 3rd or a lighter gauge can help, along with a light touch.