Why can't we play the ball through the centre?

Easiest answer ever
We have no centre midfielders that are above a 6 out of 10
 
The best midfield performance I’ve seen from us in recent memory involved Donny, Matic and Mata. Bruno and Pogba undoubtedly more talented but they don’t have the willingness of ability to move and take the ball under preasure. Ok Pogba does but he is often too slow to get in to space and then there is no movement around him for quick passing interchanges.

On top of that when there actually is someone making decent options we then don’t play the pass. It’s a total cluster feck and honestly I wouldn’t be that upset if we sold our entire midfield.
 
We lack the players suited for it, well actually we have them but we shun them in favour of individualistic/flashy and hardworking midfielders and attackers
 
A couple of reasons:

-We do not have an involved no9 who can link-up play or hold the ball.
-Our central midfielders rarely make it into the box
-Our wide players are mostly limited and don't stay wide enough to create spaces
-Our fullback don't overlap to force the opposition to shift players on that side
-We move the ball too slowly
-Our players seem like total strangers at times and can't string 3 passes together
-For every team the easiest is to defend the center

Good points. I would add 1 more
- most bottom clubs in the past 10 years, are much improved on defensive discipline, when you often see 2 lines of 4. When they seldom make mistakes, how can you explore the centre? Only teams that are committed forward will expose their centre. Ironically, every teams in the world know how to exploit City, by passing the ball behind Cancelo. How many teams can manage to score? Easy said than done.
 
Good points. I would add 1 more
- most bottom clubs in the past 10 years, are much improved on defensive discipline, when you often see 2 lines of 4. When they seldom make mistakes, how can you explore the centre? Only teams that are committed forward will expose their centre. Ironically, every teams in the world know how to exploit City, by passing the ball behind Cancelo. How many teams can manage to score? Easy said than done.

Exactly, it is better to do something obvious perfectly, than trying to reinvent football every time.

City and Liverpool are well rehearsed teams that know exactly what to do and while anyone knows what they are going to do they can't stop them. Smaller teams will eventually make mistakes, sooner on later they do that, if you don't press them aggressively you miss on a important chance to score against them.
We can't press, we are not trained to press efficiently, no manager taught our players to do that and all big teams do that. That's another reason we are so far behind. Looking at our pressing especially under Ole was disappointing to say the least, 3-4 players up front, a huge gap in midfield and defenders afraid of going further up the pitch.

Under Sir Alex, we were a dominant force because we were very good at certain aspects of the game.
 
I am a bit surprised so many people think it comes down to personnel. Most of the time in the buildup play I see every single midfielder recycling the ball back to CBs/FBs. It is clearly down to instructions.
Making McFred our nominal midfield two doesn't help for sure, but we see that when Pogba plays quite often as well. The only brave midfielder who passes through the middle is Matic, but we choose not to play him.
 
Have you seen the first touch and close control of our entire squad really?
Only Bruno, Mata and Vdb are the three players I'd trust to take a good first touch and progress the ball in the correct direction.

It also requires other players to make themselves available when the player in possession is under pressure, and they need to have a good first touch and so on.

controlling the ball on the wing is relatively easier as there's more space to receive it, because the opposition is usually tucked in, the opponent is going to be on one side only, there will be space to knock the ball towards the corner flag.