The Lunar Rider is hereditary; generally the father takes his son on as an apprentice. William Case was severely distraught over his mentor/father’s death. They were both powerful, influential leaders in the organization. While it may seem good to pass on that power, William feels its best his son stay out of that business.
Ultimately it’s Michael’s choice. If he wants to become a Lunar Rider he can just say so. Training takes years but William is in his prime; so there’s time. Michael could read the journal both William and his father keep (used in training) but he kept it well hidden on the computer. And a USB that was on him at all times. Which is why in certain parts of Ruby Caves Michael may not seem smart, but he’s just young and naïve about what’s going on around him.
And besides, werewolves are very hard to kill; and well.... Sweet Brown puts it best at 00:25