Rabbi Akiva agrees with Rabbi Yossi HaGlili that animals are included in the festival food-preparation permission — but he reaches this conclusion through a different textual mechanism. Where Rabbi Yossi HaGlili uses the word akh ("only") to exclude non-Jews, Rabbi Akiva uses the phrase "for you" (lakhem).
"Only what is to be eaten by all souls" — Rabbi Akiva reads "all souls" as genuinely inclusive, encompassing both animals and non-Jews. But then comes the qualifier: "for you." This phrase, Rabbi Akiva argues, specifically excludes non-Jews. "For you" means for the Jewish community — not for gentiles.
But why exclude non-Jews rather than animals? Rabbi Akiva provides the decisive reasoning: "For you are exhorted over the beast, but not over the gentile." A Jew has an explicit Torah obligation to care for and feed his animals. The commandment to provide for one's livestock is not optional — it is a binding legal duty. No such parallel obligation exists toward non-Jews in the context of festival food preparation.
The principle underlying Rabbi Akiva's ruling is that obligation determines inclusion. The scope of what you may prepare on the festival follows the scope of what you are commanded to sustain. Since the Torah commands you to feed your animals, cooking for them on the festival is permitted. Since no comparable command exists for non-Jewish guests in this context, "for you" excludes them from the permission.