My books on ibooks on my phone are NOT showing up on my mac yet I have it set to sync and other books ARE. Why is this? It wants me to REpurchase a book I already purchased

What have you set to sync, and what 'other books ARE' ? The sync bookmarks and collections settings do not copy books between devices/computers, all the 'sync collections' setting does is if you have a book downloaded on both and you move into a collection on one of them, then it will be moved into the same collection on the other.

If you are using the same account that you bought the book with, and you haven't moved countries since buying it, it should show in the Purchased section on your Mac's iTunes for redownloading on it (unless you've hidden it from the cloud) : click on the Purchased link under Quick Links on the right-hand side of the iBooks Store homepage. Or connect your phone to your Mac's iTunes and do File > Devices > Transfer Purchases, and then do File > Move Books From iTunes in your Mac's iBooks app.