There is nothing in the Prophet’s Sunnah to indicate that it is not allowed to speak whilst eating. The popular saying among some, that there is “no greeting and no talking over food” has no basis in sharee‘ah.
It is proven that the Prophet (blessings and peace of Allah be upon him) talked whilst eating.
In al-Bukhaari (3340) and Muslim (194) it is narrated that Abu Hurayrah said: One day some meat was brought to the Messenger of Allaah (S) and the foreleg, which he used to like, was offered to him. He took a bite, then he said: “I will be the leader of mankind on the Day of Resurrection. Do you know why that is? … Then he quoted the lengthy hadeeth about intercession.
In Saheeh Muslim (2052) it is narrated from Jaabir ibn ‘Abd-Allah that the Prophet (blessings and peace of Allah be upon him) asked his family for condiments and they said: We do not have anything but vinegar. He called for it and he started eating it, saying: “What a good condiment vinegar is, what a good condiment vinegar is.”
Al-Nawawi said: This shows that it is mustahabb to talk whilst eating, so as to put the diners at ease.
End quote from Sharh Saheeh Muslim (14/7)
Putting diners at ease, which is mentioned by Imam al-Nawawi (may Allah have mercy on him) here, is something that is well known and prevalent among the Arabs, because it is part of honouring the guest and showing generosity to talk to people whilst they are eating, especially guests.
Ibn al-Qayyim said: The Prophet (blessings and peace of Allah be upon him) used to speak whilst eating, as seen above in the hadeeth about vinegar, and as he said to his stepson ‘Umar ibn Abi Salamah, who was eating with him: “Mention the name of Allah and eat from that which is closest to you.” End quote from Zaad al-Ma‘aad, 2/366
In these hadeeths there is evidence that it is permissible to speak whilst eating. As for the hadeeths that mention the command to speak whilst eating or that forbid doing so, none of them are saheeh.
Al-Haafiz al-Sakhaawi said: I do not know anything about it, either forbidding it or approving it. End quote. Al-Maqaasid al-Hasanah, p. 510
Shaykh al-Albaani (may Allah have mercy on him) said: Talking whilst eating is like talking whilst not eating: good talk is good and bad talk is bad. End quote from Silsilah al-Huda wa’l-Noor, tape no. 15/1
And Allah knows best.