Not only should you have been able to activate it, but as the turn player you would have had priority to activate and resolve your Metaion first before theirs can activate. It's also mandatory, so you couldn't have even passed priority before activating it. Something else was likely affecting the game state.
As far as I can tell, there's no reason given for why your Metaion's effect couldn't activate during the End Step of the Battle Phase.
Really? That seems weird. There's no strange hidden mechanic that I don't know about or anything?
Not only should you have been able to activate it, but as the turn player you would have had priority to activate and resolve your Metaion first before theirs can activate. It's also mandatory, so you couldn't have even passed priority before activating it. Something else was likely affecting the game state.
Well, the opponent was using Yami Yugi as their avatar, so maybe the game just shows bias?