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.