You're asking an excellent question! But interestingly enough, there's no clear indication from the text that Jacob withheld food from Esav.
On the contrary, the verses indicate that Jacob actually did give his brother Esav food immediately when he saw his brother starving. The verse says (Gen. 25:33-34), "He (Esav) sold his birthright to Jacob, and Jacob had (already) given Esav bread and lentils..." According to the rules of Hebrew grammar, "had given" is past perfect, meaning that when Esav sold the birthright for money, Jacob had already given him free food! (Rabbi Yaakov Tzvi Mecklenburg)
But even if we assume that Jacob withheld the food, why would he do that? The Talmud states, "Rabbi Yochanan said: Five sins that wicked one (Esav) transgressed on that day — adultery, murder, heresy, denial of the future resurrection and despising of the birthright."
Jacob knew who his brother was. The birthright included the privilege to lead the family in the service of God. Esav was totally unworthy to serve God. Jacob knew He would desecrate that service. The very fact that Esav sold the birthright showed just how unworthy of it he was. Therefore, Yaakov saw this opportunity as an obligation to relieve Esav of the birthright.
