While eating food, the respiratory path from our mouth closes. But when we talk while eating,it opens as the sound comes from the larynx. So, there food goes down the trachea which results in coughing and choking.
We are advised not to talk while eating because, if we talk while eating, the larynx opens. Instead, of going to the food pipe, the food may go to the larynx. Then, it results in coughing. The voice comes from this tube, and also, it is placed first. If we want our food to go to the food pipe, the larynx must be closed.

Thank you.
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