This is an act of veneration to Annadevatā, as well as thanking Paramātmā for providing a square meal.
Why should one not eat or drink anything which has been eaten or drunk (‘enthu’) by somebody else?
Eating a half-bitten fruit or sandwich or drinking juice from a container which has been lipped previously by a relative or friend amounts to ritual impurity. Something which is ‘enthu’ does not conform to the shāstras’ ideals of āhār shuddhi (Yājnavalkya Smruti 1-6-162).
Essentially, when one eats or drinks, one is ideally offering this to the Paramātmā within (the Antaryāmin). Therefore this should be pure. In the BAPS Swāminārāyan philosophy, one is offering food both to Pramukh Swami Mahārāj – who is one’s Akshar-rup ātmā, and Bhagwān Swāminārāyan, who manifests in him.