But among all the B’nei Yisrael, a dog will not sharpen its tongue at man or animal. You will then know that Hashem distinguishes between Egypt and Yisrael.

You shall be men of holiness to Me, and you must not eat flesh that was torn off in the field. Throw it to the dog.

"flesh that was torn off in the field..."

Since the dog gave it's life [to guard sheep from becoming] terefah when the wolf came to attack it, you will not be ungrateful to it, that when you have terefah you throw it to [the dog] as a reward for successfully guarding it until now, and for guarding all the other {sheep]. Because that is the way of the world to set dogs to guard the flock from the wolves:

Why did dogs merit that of their excrement sacred books and tefillin should be made? Because it stated, But against any of the children of Israel shall not a dog whet his tongue.

...and even though animals have no reward and punishment, because they act on natural instinct [and do not have free will], G-d said to give it its reward. From this a person can learn a lesson to know the ways of G-d, that how much more so there is a reward and punishment for a person who has free will.

...do not eat from a place where a rat or a cat has bitten, for that too is harmful to your memory.

The students of Rabbi Elazar asked him: For what reason does a dog recognize its master, while a cat does not recognize its master? Rabbi Elazar said to them: If it is established that with regard to one who eats from that which a mouse eats, eating that item causes him to forget, with regard to the cat, who eats the mouse itself, all the more so does eating it cause it to forget.

"a cat does not recognize its master." This is confusing according to the stories that are told in the book "Natural History" which illustrate how cats have feelings of love and friendship with their owners. And I will tell one story here and from it you will understand...

..According to this story and other stories like it, it is proven that the cat also knows its owner and does not forget them, so how can they say here that the cat does not know its owner? Therefore, it seems that Rabbi Elazar's opinion is true, and the reason for the forgetfulness of the cat that does not know its owner is because it eats mice, and therefore every cat that does not eat mice but eats from its owner's table the meat of animals, fowl, and fish that its owner gives it every day during the meal, and does not eat the mice but hunts them and sends them away, it has no forgetfulness of anything, and the disciples of Rabbi Elazar ben Tzadok were only talking about a cat that eats mouse meat.

Similarly, Rabbi Yoḥanan said: Even if the Torah had not been given, we would nonetheless have learned modesty from the cat, which covers its excrement...

And this is the same as what Rabbi Shimon ben Lakish said: There are three impudent ones: The Jewish people among the nations; the dog among animals; and the rooster among birds.