Well...
In regards to Anniversaries, the most common denominator in this discussion would be the fact that not only does Y'shua("Jesus") state that in Matthew 19:4-6 " 4 And he answered and said unto them, Have ye not read, that he which made them at the beginning made them male and female, 5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? 6 Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder. " but, that it's(being the expectation that a man will marry a woman) also stated in the book of Genesis... 2:24 " 24 Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh."; these things often regard the natural order in which God, even in various latter scriptures(Ephesians 5:28 " 28 So ought men to love their wives as their own bodies. He that loveth his wife loveth himself.", or 1 Corinthians 7:33 " 33 But he that is married careth for the things that are of the world, how he may please his wife."), expects us to obey if we are married.
I think, and I couldn't tell you for sure because I wasn't there, that in the time(s) when birthdays' and anniversaries' were first celebrated we'd definitely have to take a look at why they are celebrating these things and how they were celebrating it...
In my opinion, I'll reiterate myself, a true birthday is when a person is "born again"; that is, resurrected after the second coming. I'm not really sure that people even understand how to celebrate the birth and death of salvation... how can people be expected to compel one another to truly appreciate God, whether it's under sect influence or of their own accord, to the degrees which God really expects us to if we cannot radically exceed hypocritical standards in simple daily accordance; likewise how can people actually truly celebrate a birthday or an anniversary if in all actuality we ought to appreciate the day we're given anyway... Surely we can "love one another", and thank God for the blessings which are or were in our lives, but again I believe we can customarily appreciate and appropriately, morally, celebrate these days which people momentously mark so long as you recognize that God is the primary influence behind that marriage or birth... saying that, I'm not stating that you ought, therefore, to shun and hate any birth or marriage which isn't "sanctified" by God...
What really matters, as a Christian point-of-view, is that(in accordance to scripture(s)) people aren't given in marriage in the resurrection... and that our mind, as Christians, are focused on Christ and His doctrine.
Matthew 22:30 " 30 For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven."
All of that, and the next few words will provide your "answer": Nothing's really wrong with birthdays or anniversaries, so long as we're attentative to how and why we're celebrating them.