The majority of the scholars are of the views that celebrating one's birthday is considered bid'ah in the religion and immitation of the non-muslims.
The Prophet peace be upon him said in a saheeh hadith:
“You would follow the ways of those who came before you step by step, to such an extent that if they were to enter a lizard’s hole, you would enter it too.” They said, “O Messenger of Allaah, (do you mean) the Jews and Christians?” He said, “Who else?” (Reported by al-Bukhaari and Muslim). The Prophet (peace and blessings of Allaah be upon him) also said: “Whoever imitates a people is one of them.”
Please refer to this fatwa for a detailed explanation
Also there's a refutation for that "fatwa rahimiyyah" argument that you can watch here,