Solskjaer is hailed for having a good record against the 'big six'. In his 2 years here;

Hasn't won a game against Liverpool.
Hasn't won against Arsenal in the PL.
Lost 2-0 to City at home in PL.
Got knocked out in the League Cup by City.
Lost to Arsenal 2-0 away - twice in PL.

Lost to Arsenal 1-0 at home in PL.
Got knocked out in the FA Cup by Chelsea.
Lost 6-1 to Spurs at home (joint-record PL defeat).

Throw the draws we've had into the equation and the record looks pretty weak overall.

Aside from that, he's lost 3 semi-finals (two against 'the big six') and one to Sevilla, knocked out of the CL by Barca without having a shot on target at home and knocked out of the FA Cup by Wolves. All considered 'big games'.

We've won our fair share of games against big opposition - just like we did under every manager in our history - but it's hardly an indicator of Solskjaer being a genius.

Liverpool did the same for 30 years without looking like getting close to a title most years.

This is one of the main arguments people use when they look for reasons to stick with Solskjaer, as if we were some massive underdogs against Leicester, Spurs, Chelsea & Arsenal.

The overall record isn't as great as some make it out to be. Honestly.