I wouldn't call that poorly written. You also have to take into account that the Bible is a collection of books, accounts and scriptures written by dozens of authors, and so it is bound to have several disparities, especially between books that were written centuries or even a millennium apart. As you hint to in your reference to your poor education of the Bible at school, you clearly have a complete lack of knowledge of the theological and historical significance of the structure and style of the Bible. I can understand why though; Catholicism teaches less from the Bible and from its own traditions and doctrines (much of Catholic tradition has little to no grounding in any Biblical scripture). How much did you learn about purgatory and penance, Catholic doctrines with absolutely no grounding in the Bible? And how much did you learn about important theological concepts within the Bible such as eschatology, Christology or Logos?
It is believed the date of Christmas was decided at the time the Church was still trying to integrate Romans and their beliefs into them. They replaced existing festivals and celebrations with Christian ones and it is thought the Romans celebrated the Winter solstice on December 25th and they just changed it to Jesus' birthday. It worked so well that not only do all Christians recognise and celebrate Christmas, so do members of other religions or those of no fixed religion.Perhaps... So then, why do we celebrate Christmas on that date and why do so many people celebrate it and label it as the birth of Christ?