But you said in your OP that the cable is pushed into the connector and if you can do this, unless your supplier has an entirely new form of F plug, the cable is too small or the connector is too big (same thing, different perspective).
My plugs are fitted as per the link and, without the use of a tool of some kind they will not pull off. Now you are saying that you assaulted them in some strange fashion to produce a shear force and they failed. I don't think that they were ever expected to survive that, whatever it was.
These plugs are used in satellite dish, and in some cases antenna installations, all over the country and there are not mass complaints anywhere about them. Perhaps you should go back to the manufacturer, who is it, and ask if the plugs should pull out. It has been known for suppliers and manufacturers to sometimes make packing mistakes and as all the plugs are very similar it would be difficult to tell at a glance.
If you can push and pull the plugs off the cable with little effort something is the wrong size and you can post in upper case letters if it makes you feel better but it doesn't alter the fact that something is wrong.
Actually, I would suggest that if you can screw the connectors onto the cable using your fingers alone then the plugs are too big, mine need at least a pair of pliers and the silicon grease to get them on.