It’s just a bizarre time to show such a big match, why put your biggest game at the worst time??
Sky didn't take it with their first pick because they can only show teams 5 or 6 times at 16.30 Sun, so they took Newcastle v Man United meaning BT took City v Liverpool with their second pick, meaning it has to be at 12.30 as that's when their games have to be played. Sky have calculated that this isn't as important to use up a Liverpool Sun 16.30 first pick on as opposed to Liverpool v Arsenal, Liverpool v Tottenham, etc.
When Sky pick their 16.30 Sun game BT then have second pick, but they can also only pick teams 6 times in their one weekend package. As a result Sky work out the games they can dangle BTs way in the hope BT take them, which eventually leaves them maxed out on some big clubs leaving Sky to then have all the big games for the rest of the weekends. After this weekend Sky will know if they can't pick City or Liverpool at 16.30 Sun for quota reasons they can pick something else knowing BT can't take the City or Liverpool game, so it will bounce back to Sky to stick at 14.00 Sun, 17.30 Sat etc with a lower pick.
This is why some big City and Liverpool games have fallen BT's way since the New Year (Manc derby, Liverpool v Chelsea and this). Sky passed them hoping BT would take them, which they did. Sky take the hit of missing a few bigger weekend games for the bigger win of having all of them in the last 10 weeks.