As everyone knows, Lurianic Kabbalah teaches that after the Shviras Hakeilim - The Breaking of the Vessels, Nitzozos Hakedusha - Sparks of Holiness, flooded the world and went into everything in creation. The Arizal taught that recapturing these Nitzozos can be done through the use of these objects for a mitzvah.
Included in all objects are animals as well. Thus, when one eats food for a mitzvah, be it for a Holiday meal, or to give one strength to learn Torah, that action captures the Sparks and raises it on high.
However, this raises a dilemma. How can one recapture the Sparks from food that is non-kosher which one in not permitted to eat?
The Bnei Yisaschar (ח"ב דף צ"ה ע"א.) makes a famous statement: one who abstains from eating food that had non kosher food fall in, but was nullified through the rule of Bittul B'Shishim ie. The non kosher is less that 1/60 of the kosher food, is an Apikores - a non believer in the Torah. The Bnei Yisaschar explains that since our job in this world is to recapture those Holy Sparks, he who demurs from eating this food actually rejects the entire premise of the Torah itself.
This is clearly the interpretation of the Mishna cited above, "Ohev es Habriyos, U'mekarvin Le'Torah" that the true "drawing creatures close to the Torah" is through this process of recapturing the Holy Sparks, which through it we show our devotion to the Torah and its mission statement for us.
Regarding non food items, as again we all know (of course) that R Chaim Vital in the Sefer Shaar HaGilgulim quoting his master the Arizal, every creation can be a reincarnation of a previous soul which needed a Tikkun. So therefore to mekarev them to the Torah ie. Giving them their needed Tikkun is the greatest form of Kiruv to the Torah one can possibly do.
Based on this principle, Rav Aharon Bina Rosh Yeshiva of Netiv Aryeh in the Old City is careful, when faced with a cat or animal crossing his path to exclaim "I Am Mochel You! - I absolve you from your sins!" Thus perhaps giving the animal their much needed tikkun.