Why was Henry Carey not acknowledged by Henry V111?

There are many reasons why King Henry never acknowledged Henry Carey. It is possible that King Henry was NOT the father of Mary Bolelyn's son, as he was birthed after the affair ended. It's widely debated as to whether or not Henry was conceived within the correct timeframe to the King's son. (Meanwhile, Mary's daughter, Catherine, was conceived and birthed during their affair-- irrelevant to the question, but food for thought). It is also possible that King Henry never acknowledged Henry Carey because, upon his birth, the King had fallen in love with Mary Boleyn's sister, Anne. Admitedly marrying his own son's aunt could have been quite troublesome for the King's reputation and spiritual wellbeing, which is held to the highest esteem.