I *think* it's because Griezmann was offside for the original cross and the defender possibly only headed the ball because he was doing so to stop the ball reaching Griezmann. It seemed to go to the on-pitch ref rather than a simple VAR overturn because there was interpretation over whether the defender had headed the ball because he was concerned Griezmann was going to get on the end of the cross. He didn't, he headed it as the onside player he was marking would otherwise have scored.
I guess the VAR officials asked the referee to decide if the defender's decision making had been affected by Griezmann's (offside) presence. The on-pitch referee thought it had
It didn't really matter anyway and it's always funny when ill-fate befalls Griezmann as he's just a naturally obnoxious person. The VAR officials should have just put Griezmann's celebration on the screen and asked the referee to decide if the goal should stand based on that.
Think back to the Spurs game and that dodgy penalty, where Kane was stood in an offside position, Lovren tried to block the pass and by playing the ball, reset the phase and then this played Kane onside. We all went mad, but PoP explained the rule and while its bollocks, Kane being where he was isn't an offence within the laws, once Lovren played the ball. That goal last night was the same and should have stood.
That's also not how it works. The problem for us is that Lovren attempted to play the ball. If he'd stood still and it rebounded off his leg, Kane would have been called offside (by the LOTG). But by attempting to play it, he negated the offside. It's dumb, but that's what the interpretation is.
The offside law is shite - City away for their 2nd last season, about 3 were offside from the freekick, all in Ali's line of site, but because the ball cleared the lot and went to Jesus, none where classed as interfering with play, which is bollocks.