"It/Its"- is used for neutral gender (eg: Hang the picture there. It look much better.) -is also used for unknown gender (eg: animals) Eg: Give the dog its cushion.

the possessive pronouns for animals is "Its" (neutral) but if the animal is identified, you know the gender you can use "his" or "her"... in your example :" It is his cushion" because obviously you are talking about your dog or cat...

"it's its cushion" is perfectly good English. However, you don't hear this very often because people tend to anthropomorphise, even when they don't know the sex of the animal.They tend to know the sex of their own pets, so 'his' or 'her' is used.

The pronouns: she, he and it she is the pronoun for female animal and he is the pronoun for male animal. It is the pronoun for something that doesn't has live.

'Its' is used in the case of a neutered animal. If the dog is male, you can say my dog Spot likes his cushion. If your cat is female then you say, my cat Fluffy likes to drink her milk in the morning.