Explanation: "Home"

HOME

"Home" can be used as an adverb of place. 

-It means "toward the direction of home".

-Note also We DO NOT need a PREPOSITION with HOME when it is used with any VERB referring to

direction like GOING.

For example:
My father is going home. 

- "home" is an adverb in this sentence thus we don't use any prepositions. 
- "going" is a verb referring to direction

AT HOME

Once you arrive home, it means you are then "at home".

-NO MORE DIRECTION is suggested

-So, AT is then the APPROPRIATE PREPOSITION to use with home.

For example:
A: Will you be at home tonight or are you going out? 
B: No, I'll be at home. I'm going to read a book.

Note, in spoken American English, we may hear "I'll be home tonight." - "AT" is omitted.
It's okay to do this omission of AT but not in FORMAL ENGLISH.