Why don't we use an apostrophe to denote ownership on 'it'? [duplicate]

Because its is a possessive pronoun

My head
Your head
His head
Her head
Its head
Our heads
Your heads
Their heads

Just because its ends in an "s" doesn't mean it takes an apostrophe.
To use your example, even though the claws belong to the cat you wouldn't write:

The cat licked hi's claws.

Similarly, you don't write:

The cat licked it's claws.

Additional info

'It' has a number of different meanings and it's easy to confuse them. The easiest way to understand its role is to replace it with a similar 'place' word to understand the pattern.

Where am I? - I am here.
Where are you? - You are here.
Where is he/she/it? - He/she/it is here.

Your example I looked at it shows a different function:

You looked at me
I looked at you
I looked at him/her/it

So you can see that it can be replaced by he/she or by him/her depending on the construction of the sentence.

In your original sentence its can only be replaced by my/your/his/her/our/your/their. None of these takes an apostrophe, and neither does its.