There is a word Bid'ah in Islam and it means innovation in religious matters. Some Islamic scholars says that birthday is Bid'ah as it was not celebrated by any of the prophets, apostles and their companions so if we celebrate it then it connotes that we are followers of Bid'ah. But, I am always urged to think that Birthday's celebration doesn't belongs to religion and nor there is any rulings about birthday's celebration in Islam then why is it said to be prohibited?. We know very well that innovations are much here as compared to the era of prophets, companions and companions of companions. For instance, Hazrat Bilal (Rz) never used electronic mikes to pronounce Adhan, There were no guns usage in wars etc. But today, guns are used and mikes are also used but they are not called Bid'ah. Then why call birthday's celebration Bid'ah?
Now, when there is no answer to this, the scholars show the ayah of Koran as stated,
“Follow what has been sent down unto you from your Lord, and follow not any awliyaa’ (protectors, helpers, etc.) besides Him. Little do you remember!” [al-A’raaf 7:3]
And I have also an answer to this argument which is quite logical. My answers says that the God, here, commanding us to not follow something beside' about which God has given order.
For instance God has declared that fast is what during which a believer has to stay hungry and thirsty till a certain time. But if anyone says that we can drink and can't eat during fast or vice versa then, to me it is actually Bid'ah and celebration of birth is not so because no any restrictions have been made by God about this nor there are commands that oppose birthday's celebration.
There are other Ayahs which are placed before us be like argument and that is,
“O you who have believed! Do not take the Jews and the Christians as allies. They are [in fact] allies of one another. And whoever is an ally to them among you – then indeed, he is [one] of them. Indeed Allah guides not the wrongdoing people.” [Koran 5: 51]
"And be not like those who forgot Allah, so He made them forget themselves. Those are the defiantly disobedient." [Koran 59: 19]
“Follow [O Mankind] what has been revealed to you from your Lord and do not follow other than Him any allies…” [Koran 7: 3]
Hadiths related to current argument:
“He who imitates a people will be from among them (on the Day of Judgement).” Anonymous
[Abu Daawood] And in another narration, he sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) said: “The one who imitates people other than us (i.e., in faith) is not from us. Do not imitate the Jews or the Christians.” Anonymous
Again I arise a question here that what if I discover a day, say "pencil day" and I announce it's celebration every year. Since I am a Muslim other than Jewish and Christians thereby the peoples can follow me and celebrate this day. And as far as my knowledge is concerned, I don't think that the imitation of a Muslim is prohibited in Islam... So my argument says that the Ayahs and hadiths quoted above must be telling us something different.
What I think is that it may be disliked to attempt imitation and not Forbidden.