The rabbi asked me, "Are you buying this for yourself to eat or for your dog?" He explained that it is not forbidden for Jews to possess pork. It was only forbidden for Jews to eat pork products. He went on to explain that the Talmud expressly states that if a Jew has pork, he should feed it to the dog. Since I had a dog, this would follow the Talmudic instruction.
The rabbi also noted that this rule was in contrast to feeding the dog a mixture of milk and meat. Jews are expressly prohibited from deriving any benefit from mixing milk and meat. That, he explained, included feeding it to a dog. Over the next days I began to question: Why would the Talmud expressly direct Jews to feed pork to the dogs? Certainly, the Talmud would not direct a Jew to perform an act that violates the laws of Kashruth.
I sought a clue from the Midrash (a compilation of Rabbinic literature from roughly 400 to 1200 C.E). The Torah states that just before imposing the Tenth Plague upon the Egyptians (killing of the first born), God told Moses that while there would be loud wailing throughout Egypt, but that where the Hebrews lived, not even a dog would bark.

The Midrash states that just before the Angel of Death descended, God instructed the dogs living amongst the Hebrews to be silent. The dogs complied with loving obedience. God was so impressed that He told them that because they had obeyed with such love, He would reward them. He would instruct the Jewish people that hereafter they should give their non-kosher food to the dogs.

This explains giving non-kosher food to the dogs in general. However, the Talmudic directive deals only with Pork. It does not mention other non-kosher foods as rabbits, shrimp or lobster, etc. Thus, this Midrashic
story did not explain why the Talmud instructs Jews specifically to feed pork to the dogs.
The first night of Passover arrived. As I began to eat the Seder meal, I thought to myself, that this was the first time I had ever attended a Seder which had truly kosher food. And I thought of my dog at home, who was eating his beef and bacon. Suddenly! The answer came to me in a flash!

We are told to feed pork to the dogs because pork is Kosher for dogs. The Talmud does not tell us to feed pork to Gentiles. That is because the laws of Kashruth do not apply to Gentiles. However, the Talmud gives us a directive to feed pork to the dogs, so it must be that Pork is a kosher food for dogs! (When I returned home, I had to tell my beloved mutt, Duke, "Sorry, boy, no more cheeseburgers. But here, enjoy a ham sandwich! Oh, by
the way, Duke, since it is Passover, your ham sandwich is on Matzo!"
In conclusion, while pork is certainly not Kosher for a Jew to eat, it is Kosher for our beloved pooches. Thus, by feeding pork to our dogs, we are actually helping them to keep kosher! A Mitzvah in and of itself!
A very joyous and Kosher Passover for you - and for your dogs!
P.S.: A point to ponder: Does this mean that we should make sure that the pig was properly slaughtered in a kosher manner, and that it was salted and soaked? Do we need a Shochet? I'll have to ask my Rabbi!