PROOF NO 1
Book 006, Number 2606 (Sahih Muslim)
Abu Qatada Ansari (Allah be pleased with him) reported that Allah’s Massenger (may peace be upon him) was asked about fasting on Monday, whereupon he said: It is (the day) when I was born and revelation was sent down to me.
This Hadith is also reported in by Imam Bahayqi in his “Sunnan ul Kubra” (vol. 4, pg. 300 Hadith no 8182, 8259), in the “Sunan” of Imam Nisai and the “Musnad” of Imam Ahmad bin Hanbal.
It is clear from this Hadith that the Holy Prophet (saw) was very happy about the day of his birth and so fasted out of gratitude. Fasting is a form of worship, so one can celebrate this day by any form of ibada. One can fast or hold gatherings or provide food to the poor, all being acts of worship.
PROOF NO 2
Volume 7, Book 62, Number 38: (Sahih Bukhari)
Narrated ‘Ursa; 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.”
Abu Lahab freed Thuwaiba on joy at birth of Prophet (salallaho alaihi wasalam), even the worst of Kufaar and greatest of enemies is given relaxation in his Adhaab due to freeing Thawaiba by pointing with his finger, so Imagine the situation of a momin who rejoices on Mawlid, detailed explanation of this hadith shall be given in the last section of Verdicts from classical scholars.
PROOF NO 3
[Sunnan an Nasai’I, Volume 1, Page No. 450, Hadith No. 450]
Hadrat Anas bin Malik (ra) narrates that Prophet (saw) while mentioning his journey of Miraaj said: Jibril (a.s) asked me to get off from Baraak at Bethlehem and told me to say the prayer there, after which he said: Do you know where you have prayed (O Messenger of Allah)? You prayed at Bethlehem where Isa (a.s) was born.
So the Mawlid, the places where Prophets(A.S) are born are amongst Sha’ir (sings to be venerated) of Allah.
So here Allah himself says to Rejoice and be happy on such a day , As its Sunnah of friends of Shatan [devil] to cry on such a day.
In Sahih Muslim, Volume 2, Page No. 147, Hadith No. 1130 (Dar ul Kutab al ILmiyyah)
Ibn Abbas “Allah be pleased with him” reported: The Prophet “Allah’s blessing and peace be upon him” came to Madina and saw the Jews fasting on the tenth day of Muharram. They were asked about that. They replied: “This is the day, on which Allah made Moses and the children of Israel emerge victorious over Pharoah. So, we fast on it “OUT OF GLORIFICATION TO IT”. The Prophet “Allah’s blessing and peace be upin him” said: “We have more claim over Moses than you.” So, he ordered Muslims to fast on it
If Jews glorify their days to venerate Musa (a.s) then we Muslims have more right to venerate and rejoice on day when Prophet (saw) was born, this is an accepted analogy as Ulama has derived this specific ruling from the hadith, which shall be mentioned in the last section with detail.