Okay, everybody is having problems right now. I'm so surprised I found a fix for it. Instead of trying to update from the mod from the Workshop or steam itself, open up the ARMA 3 LAUNCHER. After that, go into the mods area from that and make sure the Breaking Point mod is checked. After about a minute, it should realize something is not quite right and begin to update the mod from THE LAUNCHER.

After the launcher finishes updating, it will say "Ready, update queued." From there, exit the ARMA 3 launcher and go into your steam library and Steam should automatically begin to update. Hope this helps guys!