Is it wrong to celebrate birthdays, anniversaries, and other such days?

No, such days have no religious connection or sinful purpose, so God does not care; they are matters of Christian liberty left up to each man’s conscience. Abraham threw a great feast when Isaac was weaned (Gen 21:8), and Job’s children had birthday parties (Job 1:4-5). It is Jehovah’s Witnesses that overreact in such matters, just like they overreact and condemn any and all oaths and swearing, which God’s people observed in both testaments. National holidays are acceptable for Christians, for Jesus attended a national holiday not taught in Moses’ law – the celebration of Hannukah or the cleansing of the temple by the Maccabees (John 10:22-23).