sorry
...get a bit stressed when at work. Wish I could draw a picture but skills not good enough. Reason for adding in the rocket etc was that the same principles apply and thought it easier to picture. The pressure on the inside of the nozzle will be backwards (normal to wall ignoring friction), so if the nozzle broke it would fly backwards. However there is a hole in the nozzle. View the whole thing as a lump of dumb metal: it doesn't 'know' about the conservation of momentum, the only thing which affects it are the forces acting on its physical surfaces and all forces count.
Now release your grip on the cone a little bit and blow really hard until you no longer hold the nozzle.
If the nozzle is producing thrust it will force its way into your mouth.
It is producing thrust and pushing it and you backwards slightly.
But it will actually fly out and away from you.
Well yes, because of the pressure on the inside acting backwards. Because there is no front surface (where your mouth just was) there is no front surface on which the internal pressure can act so all forces are rearward. Same is true in a rocket nozzle except that there is a front surface of the whole chamber opposite the nozzle on which the pressure can act, so the force on the nozzle (and any back face) is indeed rearwards but then there is this hole (no metal so no force), imbalance = thrust.
This is because the aerodynamic force on the nozzle is drag acting downstream.
Conventionally drag infers force due to motion, motion gives shear, shear gives lateral force on surface. Its pressure which gives the overwhelming force.
So if the force on the nozzle is drag, how does it increase the thrust?
Need a way of having hole at the back while letting gas out while keeping internal pressure high at that all important front internal surface (where the pressure pushing forward on the wall acts).
Nozzle is a means to an end, net thrust is generated elsewhere.
Always pressure, - don't shout at me for introducing kitchenware as well as bypass engines- but if you have a cupboard with two doors, slamming one shut may pop the other open but its not the 'rush of air' which pushes, its the rush of air which decelerates on getting to the door which then increases in pressure until the pressure pushes the door.