"My cat doesn't have to wash itself."
Translation:Mi gato no tiene que lavarse.
Point of grammatical order: you still have to append the correct pronoun, even to the infinitive form of a reflexive verb. For example:
- I have to wash up. = Tengo que
(Not 'lavarse'. "Tengo que lavarse" would mean that I have to wash him, her, a pet or other living creature, you [Usted], or any combination thereof.)
In this case, 'person' identifies who is performing the action, relative to the person talking about it.
First person: the speaker is involved in the action. (Singular: "I/me"; plural: "we/us".)
Second person: the person or people being spoken to are the ones involved. (Singular: "you"; plural: "you" or "you all".)
Third person: everyone else. (Singular: "he/him, she/her, it"; plural: "they/them".)
(Remember also that in Spanish, although 'Usted' technically means 'you', it's conjugated in the third person, same as 'él' and 'ella'.)
The point the OP was trying to make (similar to my response, which is currently below your post) is that both the verb conjugation and pronoun choice have to match both personhood and plurality, in both Spanish and English.