Establishing different, innovated celebrations, such as birthdays, new years, mothers day and the likes, is forbidden from three angles:

Celebrations Have Been Legislated in Islām^[1]

This is an innovation which has not been legislated [by Allāh]. Instead, it is people who have legislated it based on their own whims and desires. Celebrations and what occurs within them of happiness and joy is from worship. Hence, it is impermissible to innovate anything new in that regard, nor is it allowed to affirm and be pleased with such [invented celebrations].

Islām Has Only Two Legislated Days of Celebration

There are only two [legislated] celebrations which occur within the year for Muslims:

ʿĪd al-Fiṭr: where the people rejoice in completing their fasts.
ʿĪd al-Aḍhá: al-Naḥr, and the following days of Miná.

Aḥmad, Abū Dawūd, al-Tirmidhī, al-Nasāʾī and others [amongst the scholars] collect with an authentic chain of narration, from ʿUqbah b. ʿAmir, from the Prophet (صلى الله عليه وسلم) that he said, “The day of ʿArafah, the day of al-Naḥr, and the [proceeding] days of Miná are our ʿĪd, the people of Islām.”^[2] Additionally, the two Shaykhs (i.e., al-Bukhārī and Muslim) report from the Prophet (صلى الله عليه وسلم) that he said, “Truly, for each nation is their ʿĪd, and this is our ʿĪd.”^[3] That is, the Muslims. The attribution indicates the exclusivity of [certain] celebrations to [certain] religions.

The Impermissibility of Imitating Non-Muslim Celebrations

This practice is a resemblance of the disbelievers from the People of the Book (i.e., Jews and Christians) and other than them as it pertains to innovating celebrations not legislated [by Allāh]. Indeed, there lies no doubt that we are commanded to avoid resembling them (in that which is specific to them), and to sever the ties of resemblance between us and them as it relates to this matter.^[4]