Is it proper/right to say, 'Come and eat (Come join me at the table) if you don't mean it?

Funny – ‘Come chop’! ‘Come and eat’!

This issue has brought heated arguments between me and my friends back then in school. The issue is: when you are about to eat and you ask the people around you, ‘Come and eat,’ is it out of formality or do you really mean it? There are different schools of thought:

1) It’s mere formality just like when say, ‘Good morning’
2) It’s cultural. It is said that in some cultures, it’s impolite to eat your food without inviting the people around you.
3) It’s hypocritical or insincere to invite someone to join you at the table when you don’t really mean it. You should invite people only when you mean it, because, what if the person(s) decides to join you when in actual fact you don’t want them to. Won't that amount to telling a lie?
4) It’s greedy not to invite people around you to join you at the table.
5) It’s a sign of generosity and kindness to invite those around you to join you even when the food is too small to share.
6) It’s the nature of some who do not like to eat alone. I know a friend who said he does not like to eat alone, so whenever other people are around, he sincerely invites them to join him. He prefers eating with others.

What school of thought are you? Is it one of the above, some of the above, all of the above, or none of the above? This na B.Sc question o. Allow me relate one story:
It happened in UNIBEN years ago. One boy in the boys’ hostel was so hungry and it seemed he had no money on him. So he decided to visit a female friend in the girls’ hostel. When he got there his friend was not around but he met the room-mate. At first he was disappointed. But then he noticed the room-mate was about to eat. This guy thanked his stars for being so fortunate. This guy then offered to wait for his friend who was away. The lady in the room, after serving herself to eat, invited this guy to eat out of mere formality. She thought the guy was one of those guys who play ‘the Big Boy’ even when they are hungry. To her great surprise, this guy not only accepted, he positioned himself to join in the meal. This guy ate and ate and ate. ‘Hunger na bad thing ooo’. The guy threw courtesy and decency to the wind; he ate until he was filled. The girl confessed to her friends, ‘See me, see wahala! I invited this guy out of mere courtesy o. This guy come finish my food.’ So, here lies the question: Was it the right thing to do, inviting the guy to join her when she had no intention of sharing her meal? What do you think is the right thing to do: to invite or not to invite? ‘Come chop, na bad thing?’

I posed the above questions to my Facebook friends sometime ago. Here's a summary of their responses:

S.A -  I don't invite when I know I'm not ready to share. period

P.A - Feel @ home nor mean say mk you break Tv....if i call u come chop nor 

mean say make u finish my food u go use ur mind

M.O - I only invite wen I want to cos I wouldn't want to share "bad-bellely"but cheerfully

J.O - But seriously me no sabi form sha, if i want u to come & join me i'll call u. But if i don't want u to, i'll wait until u go b4 bringing out d food. No be by force.

Z.E.O - But,it's a nice thing eating wit ur friends. Infact, it makes me eat more.

G.P - If I invite u, I sincerely want u to eat wt me. If d fud is small, I'l kip it till u're gon n get somthng else 4 u.