The author is not questioning whether one fact can be deduced from the other. The author is asking :

How are we to identify facts? How do we count them or distinguish them?

Note that he is using the word identify here in the sense of equality - to identify one expressed fact with another expressed fact as one and the same fact. He is asking "how do we know when we are expressing the same fact in two different ways" so that we may count them and distinguish them.

With this in mind, it should be clear how the example given highlights this problem. (Note that "there is an animal in my house" does not necessarily entail "the cat is on the mat".)

I read the quoted text so that the author is not questioning whether one fact can be deduced from the other. The author is asking :

How are we to identify facts? How do we count them or distinguish them?

Note that he is using the word identify here in the sense of equality - to identify one expressed fact with another expressed fact as being one and the same fact. He is asking "how do we know when we are expressing the same fact in two different ways" so that we may correctly count them and distinguish them.

With this in mind, it should be clear how the example given highlights this problem. (Note that "there is an animal in my house" does not necessarily entail "the cat is on the mat".)