Your neighbor has certain Obligation weather he is Muslim or a Non Muslim.
There is no point of doing any unjust/ Harm/ cheating to anyone weather Muslim or Non Muslim. Every life and hon our is respectful.
That person was not a Muslim and he refused so Prophet didnot Obliged him. Allah said to Ibraheem that I was feeding him for years even if he was not taking my name........and you could not feed him even for once.
IKRAM E MUSLIM (Muslim relation with a Muslim)
The relationship of the Muslim to a Muslim more sacred than any relationship, even that of blood, culture or nation. The relationship between the Muslims is a sacred one.
Our beloved Nabi (Sallallahu Alaihi Wasallam) said: “ A Muslim is the brother of a Muslim. He neither oppresses him nor humiliates him nor looks down upon him. The piety is here, (and while saying so) he pointed towards his chest thrice. It is a serious evil for a Muslim that he should look down upon his brother Muslim. All things of a Muslim are inviolable for his brother in faith; his blood, his wealth and his honour.” (Sahih Muslim Book 31, Number 6219)
Love and Enmity for the Sake of Allah Only
The most vivid example of this is that of the Prophet Nooh (A.S.) and his son. Allah tells us: “And Nooh called upon his Lord, and said: "O my Lord! surely my son is of my family! and Your promise is true, and You are the most just of Judges!" Allah said: “O Nooh! Lo! he is not of your household; lo! he is of evil conduct, so ask not of Me that whereof you have no knowledge. I admonish you lest you be among the ignorant.” (11:45-46)
Here was the Prophet‟s own son, and Allah was telling him that the son's disobedience had effectively removed him from the family unit and from Allah's protection. How did Nooh (A.S) react to this? Prophet Nooh (A.S.) said: "O my Lord! I do seek refuge with You, lest I ask You for that of which I have no knowledge. And unless You forgive me and have Mercy on me, I should indeed be lost!" (11:47)
"This day nothing can save, from the command of Allah, any but those on whom He have mercy!” 11:43
The Prophet was true to his character, recognising the wisdom of Allah over his own judgement, and he sought forgiveness for his assumption.
Another example of this is Prophet Loot (A.S.). He fled his city by Allah's command, and tried to save his family, but this was not the will of Allah, for his wife was not of the believers. "But we saved him and his family, except his wife: she was of those who lagged behind" (7:83)
Here we see that Allah did not save the wife of the Prophet. He had to choose between obeying Allah and saving his wife, he had no choice, he obeyed Allah. He knew that the only relationships that exist are those for the sake of Allah - seeking His Great Pleasure.
Rasulullah (Sallallahu Alaihi Wasallam) said: “A person visited his brother in another town and Allah deputed an Angel to wait for him on his way and when he came to him he said: 'Where do you intend to go?' He said: 'I intend to go to my brother in this town.' He said: 'Have you done any favour to him (the repayment of which you intend to get)?' He said: 'No, except that I love him for the sake of Allah, the Exalted and Glorious.' Thereupon he said: 'I am a Messenger to you from Allah (to inform you) that Allah loves you as you love him (for His sake).'” (Sahih Muslim: Book 31, Number 6226)