The reality of the situation is very simple. Ben White was just not fit, nor ready to play in the game against Spurs during the moment where it would have made sense to bring a central defender on.
As Arsenal’s world began to crumble as Rob Holding was sent off for a second bookable offence in seven minutes, Mikel Arteta decided not to make the switch almost all coaches do when they lose a defender. It caused a stir amongst fans and pundits at halftime.
Especially considering that soon after the dismissal Arsenal conceded from a corner. The second in two matches after having previously avoided conceding from them all campaign.