When should I use 's or of for possession?

Question

I've learned in school that I should use 's only for people when it means possession. But after a while, I realized that is not true.

When should I use 's or of when the meaning is possession?

Answer 1

On the whole, 's is used more in speech and colloquial writing than in formal writing, but even for a formal essay it would be an oversimplification to say that 's should be restricted to people.

The Cambridge Grammar website observes that:

There are some general rules about when to use ’s and when to use of but there are many cases where both are possible.

It then proceeds to set out a few general principles (which are probably still simplifications or generalisations, but not as much so as your teacher's rule):

We don’t use ’s when the noun is not a person, animal, country, organisation, etc., or when the noun phrase is very long:

The name of the ship was ‘Wonder Queen’. (preferred to The ship’s name was ‘Wonder Queen’.)

The house of the oldest woman in the village. (preferred to The oldest woman in the village’s house.)

When we are talking about things that belong to us, relationships and characteristics of people, animals, countries, categories, groups or organisations made up of people, we usually use ’s:

The men’s dressing room is on the left at the end of the corridor.

The cat’s paw was badly cut.

Visit the site for further examples.

Answer 2

Sleep that knits up the ravell'd sleeve of care,

The death of each day's life, sore labour's bath,

Balm of hurt minds, great nature's second course,

Chief nourisher in life's feast ...

-- William Shakespeare, The Tragedy of Macbeth act2,scene2

There is no reason to think that "'s" should only be used for possessives involving people. In most case's "'s" and "of" can be used interchangeably.