Why celebrate wedding anniversaries but not birthday anniversaries?
Because there are no pagan origins connected to marriage. Marriage was divinely instituted by the "one true God"...Jehovah. (Genesis 2:18-24; Matthew 19:4-6; John 17:3)
Unlike the mentioned examples of birthday celebrations, the Bible does not put marriage in a bad light. Jesus himself both attended a marriage celebration and contributed to the pleasure of the occasion.—John 2:1-11.
"It thus would not be strange that a couple might on their wedding anniversary take time to reflect on the joyfulness of that event and on their resolve to work for success as a couple. Whether they focus on this happy occasion in private, just as a couple, or they have a few relatives or close friends with them would be for them to decide. The occasion should not become a mere excuse for a large social gathering. On this occasion Christians would want to be guided by the principles that apply every day of their lives. So whether one takes note of a wedding anniversary or not is a personal matter.—Romans 13:13, 14." -Watchtower 10/15/98