1.
"To not tell the truth" -> LIE
"A green fruit" -> LIME
The extra letter is 'M'.
2.
"Large, black bird" -> CROW
"Worn by a king or queen" -> CROWN
The extra letter is 'N'.
3.
"Type of weather" -> RAIN
"Railway vehicle" -> TRAIN
The extra letter is 'T'.
4.
"Used to write with" -> PEN
"Opposite of closed" -> OPEN
The extra letter is 'O'.
5.
"Faster than a walk" -> RUN
"Very old building" -> RUIN
The extra letter is 'I'.
6.
"A family pet" -> CAT
"Warm clothing" -> COAT
The extra letter is 'O'.
7.
"A long way" -> FAR
"Treating people equally" -> FAIR
The extra letter is 'I'.
8.
"Part of your foot" -> SOLE (that's pretty tricky)
"To find the answer to something" -> SOLVE
The extra letter is 'V'.
9.
"Furry marine animal" -> SEAL
"To take someone's property" -> STEAL
The extra letter is 'T'.
10.
"Part of your face" -> CHIN
"A very large country" -> CHINA
The extra letter is 'A'.
Challenge:
Here are our extra letters, collected in order: M, N, T, O, I, O, I, V, T, A.
And the clue: "A reason for doing something!".
So.. rearranging the letters gives the word: MOTIVATION.