The Psukim state that Bilam’s Donkey went off track three times. The Daas Zekeinim says that Rashi says that these ventures were a Siman of the Avos, and he explains these enigmatic words as follows.
The first time when the Malach blocked the donkey’s path it veered off to the “Sadeh” a field. This represents Avrohom who besides for Yitzchok, he had two other sets of children, Yishmael and the Bnei Ketura. The message to Bilam was, if you want to curse Avrohom’s children then go to the right or left to either of these other children, but do not stay on the middle road, which represents Yitzchok.
The second episode was when the donkey went on a narrow path between two walls and squeezed Bilam’s leg against the side wall. This narrow road which had room for only two people represented Yitzchok’s two children, Yaakov and Eisav. The donkey pushed Bilam to one side, telling him he can only curse Eisav and not Yaakov.
The last time, the Malach totally blocked the road and the Donkey had no where to go but lie down. This is the children of Yaakov who are all Kadosh V’Tahor and cannot be cursed.
