Here are the reasons, based on which this act and ANY act of birthday celebration is Haram:
Prophet Muhammad said: “Every bid’ah is a going astray and every going
astray is in Hell-fire”.
As this act was not done by Prophet Muhammad himself, neither by any Sahaba, or taboyeen, or tabe-tabiyeen, so this act is considered as newly invented matter in islam (biddat), so its haram. (please note the word "EVERY", which means there is nothing like good biddat, but every biddat leads to hell fire.. as some people believe that there is concept of GOOD biddat as well, there is not)
"Whoever imitates a group, then he belongs to them." Abu Dawood,
narrated by Hadhrat Ibn Umar (R.A).
And birthday celebration started from kuffar, its origin lies with kuffar, its did not existed in muslim world before.
As at the time of prophet Muhammad, NONE of the sahaba ever celebrated any act like that, so if someone wants to celebrate such Prophet Muhamm's birthday, then he is trying to say thet he knows MORE than the Sahaba, and he loves Prophet Muhammad more than the Sahab, which doesnt makes any sense.
Majority of scholars agree that it is Haram, based on Clear hadith and verses of Quran.
You have doubt that it is not haram? or is it fine to celebrate? then BEWARE, see this hadith:
Prophet Muhammad said:
"The halal is clear and the haram is clear, and between them are
matters unclear that are unknown to most people. Whoever is wary of
these unclear matters has absolved his religion and honor. And whoever
indulges in them has indulged in the haram. It is like a shepherd who
herds his sheep too close to preserved sanctuary, and they will
eventually graze in it. Every king has a sanctuary, and the sanctuary
of Allah is what He has made haram. There lies within the body a piece
of flesh. If it is sound, the whole body is sound; and if it is
corrupted, the whole body is corrupted. Verily this piece is the
heart." [Bukhari & Muslim]
So, based on this hadith, ONLY if you have doubt that its celebration is haram or not, then based on above hadith, Still you should avoid such act at all cost.
Rest, Allah knows the best