Shikadai is not lying but the Byakugan doesnt predict movement
Yes it does. That's literally what foreseeing attacks means. Shikadai says "Going to move". Going to is future tense. Meaning the opponent hasn't moved yet. So it is seeing how they will move. hence prediction.
Tenten also says the Byakugan can anticipate attacks, synonym for that is prediction
because it doesnt have to track movement.
That's only if the user has the 360 vision activated. We saw in the Itachi & Sasuke arc that the Byakugan user controls what aspects of their eyes are in use, as Hinata activated her 360 vision even though her Byakugan was already on.
Therefore it does not have precog.
Precog isn't even a terms used in the series. It's insight and perception, which Byakugan does better.
The only reason why Sharingan needs precog is because people can run out of your view. Sharingan is 2d vision. Byakugan is 3d vision.You cant run out of Byakugans view at any time. You are fusing sharingans ability with Byakugan. If Byakugan had precog there would be 2 outcomes.
This doesn't matter at all to whether the eye can foresee attacks. Like at all. How does whether or not Byakugan/Sharingan can see the opponent matter to whether thy can foresee attacks?
1. The precognition would be greater than an MS sharingans.
So? Byakugan was said to be above 3T in insight. As far as I know, MS doesn't grant any insight enhancements, it only grants powers like Susano or Amaterasu
2. The Bykugan would be too powerful. Noone could ever touch them in battle with any jutsu. EVER
Nope. Sasuke constantly got hit by people depsite having precog, like Naruto, Bee, Kages like Ay, etc