Push not pull
The process of peristalsis pushes, not pulls, the food down the oesophagus, and also through the small and large intestines. The muscles in the oesophagus contract behind the bolus and relax in front of it resulting in a push.
There is no mechanism for pulling food into any part of the alimentary canal. If you think about it, pulling involves something to grab on to, and gripping a slippery ball of chewed food would be pretty tricky so pushing is the only practical option. This even more the case further down the intestine where the digested food is virtually liquid - have you ever tried pulling water?