Can an owner refuse your question because you have a pet?

On Monday, the premier of the new South Wales Chris Minns has announced that, since mid -May, the owners would not have been able to refuse a potential tenant to have a pet without providing a valid reason. But, on Tuesday, his description of when the owners can and cannot refuse tenants with pets left confused.
“If the owner believes that the property is not suitable for a pet, this is a valid reason to refuse the question, it is only that it is not possible to insert the advertising that pets are not allowed,” Minns said at 2 GB.
The rental reforms will enter into force from May.Credit: The Sydney Morning Herald
The conductor Ben Fordham asked him to clarify: “So wait, but the owner can reject him if they don’t want the animal?”
“Correct, exactly,” Minns replied.
“So can you still ban pets?” Fordham asked again.
“Yes, you can, but you can’t do it automatically,” Minns replied.
When Minns said pets cannot be prohibited “automatically”, it was referring to the list of land available for the owners to allow them to legally refuse the application of an tenant with a pet. These reasons have all been included in the legislation approved in October and in force from May 19th.
What are the new reasons on which owners can pets refuse?
Minns is right to say that one of the reasons is that the property is not suitable for pets, even if the owner must say that this is due to one of the three specific reasons: there is no appropriate fencing, it is not enough open space or it would be inhuman to maintain a pet in the property.