Witnesses rejoice when a child is born. In the Bible God's people rejoiced over the birth of their children, especially their firstborn. Even Jesus showed that childbirth was a blessed, happy event among God's people (Lk 1:57,58; 2:9-14; Jn 16:21).
Just looking at the birth of Christ would tell you that it was OK for God's people to rejoice and gather together in celebration of a birth. God Himself rejoiced when Jesus was born. The angels rejoiced and gathered together and even invited the shepherds to gather!
On the other hand, you will also note that there is not even one example in the Bible of God's faithful servants who commemorated the "birthday" of anyone. Jehovah's people celebrated other anniversaries but they did not memorialize the date of birth (Jn 10:22,23).
The idea of elevating an individual just because he was born is contrary to Christian principles. Birthdays are rooted in selfish pride. Jesus gave us a guiding principle of humility not self-exaltation (Mt. 23:12; Gal. 5:26).
While we might be able to avoid the egotistical aspect, a bigger principle is involved. It is a matter of practicing unadulterated True Worship. Celebrating birthdays was unheard of by God's people for hundreds of years after Christ and only came about with the corruption of True Christianity by false teachers.
Just the slightest research would tell you that celebrating birthdays is not a practice for True Christianity:
"The celebration of birthdays has been borrowed from the practices of other nations, as no mention is made of this custom in The Bible... In fact, it was an ancient Egyptian custom."--Customs and Traditions of Israel
"Early Christians did not celebrate the birth of Christ. Birthdays in themselves were associated with pagan practices; the Gospels say nothing about the actual date of Christ's birth."--The Making of the Modern Christmas, by Golby and Purdue
"The later Hebrews looked on the celebration of birthdays as a part of idolatrous worship."--The Imperial Bible- Dictionary
One periodical stated: "The various customs with which people today celebrate their birthdays have a long history. Their origins lie in the realm of magic and religion. The customs of offering congratulations, presenting gifts and celebrating - complete with lighted candles - in ancient times were meant to protect the birthday celebrant from the demons and to ensure his security for the coming year. . . . Down to the fourth century Christianity rejected the birthday celebration as a pagan custom."
"Birthday greetings and wishes for happiness are an intrinsic part of this holiday. . . . originally the idea was rooted in magic. The working of spells for good and evil is the chief usage of witchcraft. One is especially susceptible to such spells on his birthday, as one's personal spirits are about at the time. . . . Birthday greetings have power for good or ill because one is closer to the spirit world on this day....The keeping of birthday records was important in ancient times principally because a birth date was essential for the casting of a horoscope."--The Lore of Birthdays
Celebrating birthdays was adopted from superstition and false religion which corrupted true Christianity.
The Israelites also adopted a religious practice which they renamed as "a festival to Jehovah" and "sat down to eat and drink and to have a good time" (Ex.32:1-35). Even though the Israelites used this festival to worship the True God, God still viewed this as idolatry, and that is also true of customs today that are clearly derived from false religious practices (Lev.18:3; Deut.12:30, 31; Jer. 10:2; 1Cor.10:6-11). True Christians will listen to God's thinking and avoid any association with idolatrous, corruptive non-Christian practices in their pure worship of the True God.
We are told: "Therefore get out from among them, and separate yourselves, says Jehovah, and quit touching the unclean thing; and I will take you in."-2 Cor. 6:14-18, Isa.52:11; Gal.5:9)
The only birthday celebrations of Biblical record are of pagans and linked to instances of cruelty. Hence, the Scriptures clearly place birthday celebrations in a negative light, a fact that sincere Christians do not disregard.
Consequently, while it is entirely a private matter if Christians choose to take note of baby showers or wedding anniversaries, there are good reasons why mature Christians abstain from celebrating birthdays.
As a side note, pointing to the "wise men" as a reason to celebrate birthdays requires us to be ignorant of the Scriptures. First, they were not "wise men" but "magi" or astrologers and thus were not worshipers of the True God. Second, they were not even around at the time of Christ's birth and so their gifts were not for his "birthday." Notice that he was in a "house" and is described as a "young child," not as a newborn baby.—Mat 2:1-10.