Thuwaiba was the freed slave girl of Abu Lahb whom he had manumitted, and then she suckled the Prophet. When Abu Lahb died, one of his relatives saw him in a dream in a very bad state and asked him, "What have you encountered?" Abu Lahb said, "I have not found any rest since I left you, except that I have been given water to drink in this (the space between his thumb and other fingers) and that is because of my manumitting Thuwaiba." [Bukhari: Volume 7, Book 62, (Book of Marriage kitab Al Nikah ) Number 38]The hadith of Thuwaiba is in the Sahih of Imam Bukhari, Kitab-ul-Nikah who quotes this from his own Shaykh, Imam Abdul Razzaq who was the student of Imam e Aazam, Abu Hanifah (ra). It is also quoted by Imam Ibn Asqalani in “Fath al bari”, Hafiz Ibn Katheer, Imam Bayhaqi, Imam Sohaili, Imam Baghawi, Imam Qurtubi, Imam Jawzi, Imam Mullah Ali Qari, and Imam Abdul Haq Muhaddith Delhvi (ra).
This is a Hadith, that I copied from some salafi (wahabi's) blog.
The background of this hadith is quite interpreted. Some completely deny this hadith (I don't find a reason to though), others say that it's so because Thuwaiba breastfed Prophet (PBUH) that's why. But that's hardly acceptable reason. But one thing that they mostly accept is that Thuwaiba breastfed after she was freed. (and she wasn't bound to do that because she was free)
So, some of the ulema's view and the story that Ulema tell is that Abu Lahb was happy at the birth of his Nephew. So as a matter of celebration (like we do charity or offer sweets) he came pointed at Thuwaiba (with his finger) and freed her. Thuwaiba later became His (PBUH) milk mother.
the point is, it's about interpretation. Some people can interpret otherwise. or some may deny it, I don't care. But if someone spreads words against celebrating "Milad-un-Nabi" (Birth of Prophet), then he/she will be responsible for whatever is said or spread and vice versa...
If someone is celebrating, he's not a problem (except if his way of celebration is against Islam), celebration itself is not against Islam. But if someone is spreading words against the celebration (calling it a bid'at or kufr etc), then he is spreading hatred among Muslims.
This is nonsensical to ask for a hadith that proves that Prophet of ALLAH celebrated His birthday. And I'm sure there is no hadith in which Prophet of ALLAH asked not to celebrate it. But I'm sure of one thing, ALLAH says in Qur'an, "ALLAH does not like fasaad"