Question: I know pretty well that the plural for 'person' is 'people'. But my literature professor used once the word 'persons' because, he said, he was using the word the same as it will be used 'individuals'. Or at least I understood it that way. 

So, my question is: Can I use the word 'persons' in the next phrase? (I wrote the whole phrase in order for you to have the correct context.)

> 
> I'm so into the idea of developing each skill alike, the idea of being
>  round **persons**.
> 
> 
> 

Is it okay, or should I just use 'individuals'?

Thank you! :)

Answer: 
Your sentence doesn't quite make sense and I think you need to use "individuals" if you want to refer to more than one person.

You could say:

> 
> I'm so into the idea of developing each skill alike, the idea of being
>  a rounded person.
> 
> 
> 

or

> 
> I'm so into the idea of developing each skill alike, the idea of having
>  rounded individuals. 
> 
> 
> 

You can't really use "being" with "rounded individuals" as you can't "be" more than one person.

Also, you don't say what audience this is meant for.

"I'm so into" is a very "hip" was of saying "I am very enthusiastic about". For a more formal situation you probably should use the latter.
Use 'people' in your sentence, it doesn't otherwise make sense. 'Persons' (e.g. "persons wishing to remain aboard the train...,") has an officious tone, and is really only used in that manner.