Back in 1969 Anton Lavey wrote The Satanic Bible. On page 96 (in the 1976 version) it mentions birthdays:
THE highest of all holidays in the Satanic religion is the date of one’s own birth. This is in direct contradiction to the holy of holy days of other religions, which deify a particular god who has been created in an anthropomorphic form of their own image, thereby showing that the ego is not really buried.
The Satanist feels: “Why not really be honest and if you are going to create a god in your image, why not create that god as yourself.” Every man is a god if he chooses to recognize himself as one. So, the Satanist celebrates his own birthday as the most important holiday of the year. After all, aren’t you happier about the fact that you were born than you are about the birth of someone you have never even met? Or for that matter, aside from religious holidays, why pay higher tribute to the birthday of a president or to a date in history than we do to the day we were brought into this greatest of all worlds?
Despite the fact that some of us may not have been wanted, or at least were not particularly planned, we’re glad, even if no one else is, that we’re here! You should give yourself a pat on the back, buy yourself whatever you want, treat yourself like the king (or god) that you are, and generally celebrate your birthday with as much pomp and ceremony as possible.
After one’s own birthday, the two major Satanic holidays are Walpurgisnacht and Halloween (or All Hallows’ Eve). (Lavey A, Gilmore P. The Satanic Bible. Avon, September 1, 1976, p. 96–note it is on page 53 of an online version I found also).
Early Origins of Birthdays
So what is the origin of birthdays? Where did the idea of birthdays celebrations come from?
“Originally the idea [of birthday greetings and wishes for happiness] 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 that time. Dreams dreamed on the birthday eve should be remembered, for they are predictions of the future brought by the guardian spirits which hover over one’s bed on the birthday eve. Birthday greetings have power for good or ill because one is closer to the spirit world on this day. Good wishes bring good fortune, but the reverse is also true, so one should avoid enemies on one’s birthday and be surrounded only by well-wishers. ‘Happy birthday’ and ‘Many happy returns of the day’ are the traditional greetings” (The Lore of Birthdays, Linton, p. 20)…
The giving of birthday gifts is a custom associated with the offering of sacrifices to pagan gods on their birthdays. Certainly the custom was linked with the same superstitions that formed the background for birthday greetings. “The exchange of presents… is associated with the importance of ingratiating good and evil fairies… on their or our birthdays” (ibid.).
The traditional birthday cake and candles also have their origin in ancient pagan idol worship. The ancients believed that the fire of candles had magical properties. They offered prayers and made wishes to be carried to the gods on the flames of the candles. Thus we still have the widely practiced birthday custom of making a wish, then blowing out the candles. The Greeks celebrated the birthday of their moon goddess, Artemis, with cakes adorned with lighted candles…
“The Egyptians… discovered to which of the gods each month and day is sacred; and found out from the day of a man’s birth, what he will meet with in the course of his life, and how he will end his days, and what sort of man he will be” (Herodotus, Persian Wars, Book II, ch. 82)
Since it was believed that the positions of the stars at the time of birth influenced a child’s future, astrological horoscopes came into being, purporting to foretell the future, based on the time of birth. “Birthdays are intimately linked with the stars, since without the calendar, no one could tell when to celebrate his birthday. They are also indebted to the stars in another way, for in early days the chief importance of birthday records was to enable the astrologers to chart horoscopes” (The Lore of Birthdays, p. 53). Rawlinson’s translation of Herodotus includes the following footnote: “Horoscopes were of very early use in Egypt… and Cicero speaks of the Egyptians and Chaldees predicting… a man’s destiny at his birth”…
When we examine the principles of God’s law closely, as they relate to birthday celebrations, we can understand why neither Christ, nor His Apostles, nor their true followers, observed their birthdays. As noted earlier, the practice has its origin in idolatry and the worship of the sun, moon and stars…Some may view birthday customs as purely secular, lacking any religious significance. Yet we need to be aware of the broader perspective of their origins, and the religious significance they have had—and still have—for vast multitudes of people. (Reynolds, Rod. Should Christians Celebrate Birthdays? LCN, May-June 2002. pp.16-18).
Furthermore, the book The Lore of Birthdays (New York, 1952) by Ralph and Adelin Linton, on pages 8, 18-20 had this to say:
The Greeks believed that everyone had a protective spirit or daemon who attended his birth and watched over him in life. This spirit had a mystic relation with the god on whose birthday the individual was born. The Romans also subscribed to this idea. . . . This notion was carried down in human belief and is reflected in the guardian angel, the fairy godmother and the patron saint. . . . The custom of lighted candles on the cakes started with the Greeks. . . . Honey cakes round as the moon and lit with tapers were placed on the temple altars of [Artemis]. . . . Birthday candles, in folk belief, are endowed with special magic for granting wishes. . . . Lighted tapers and sacrificial fires have had a special mystic significance ever since man first set up altars to his gods. The birthday candles are thus an honor and tribute to the birthday child and bring good fortune…
Thus it appears that birthdays had their origin in mythology and magic, with horoscopes also probably playing a role. Astrology is a really big proponent of birthdays.