Why do people say "食べる" instead of "食べましょう" or "食べよう"


From what I understand, " **食べましょう** " and " **食べよう** " both imply, more or
less, the same meaning, which is ' _to invite someone to eat with them_ ', the
latter being a verb conjugation of the volitional form, the more casual
'ましょう'.

However, " **食べる** ", the base verb which means ' _to eat_ ', is much more
commonly used for the invitation message. I would like to know why that is so,
and when have people started to use it, so much so, that is has become a
colloquial phenomenon.

Thank you.




> However, "食べる", the base verb which means 'to eat', is much more commonly
> used for the invitation message.

No. 食べる is **not** used as an invitation like ～ましょう/～よう, both of which roughly
mean "Let's eat it". The plain form is used in the following situations:

  * To state the speaker's own will

> 食べる!  
>  I'll eat it!

  * As a question to check someone's will (used with a rising intonation)

> 食べる? ⤴  
>  Wanna eat?

(Note that this **can** sometimes work as a casual invitation, but basically
it's just a question.)

  * Less commonly, as an imperative (used by a parent, teacher, etc. [Plain form as imperative](https://japanese.stackexchange.com/q/15816/5010))

> 食べる!  
>  Eat it!




> However, "食べる", the base verb which means 'to eat', is much more commonly
> used for the invitation message.

No. 食べる is **not** used as an invitation like ～ましょう/～よう, both of which roughly
mean "Let's eat it". The plain form is used in the following situations:

  * To state the speaker's own will

> 食べる!  
>  I'll eat it!

  * As a question to check someone's will (used with a rising intonation)

> 食べる? ⤴  
>  Wanna eat?

(Note that this **can** sometimes work as a casual invitation, but basically
it's just a question.)

  * Less commonly, as an imperative (used by a parent, teacher, etc. [Plain form as imperative](https://japanese.stackexchange.com/q/15816/5010))

> 食べる!  
>  Eat it!

