Haha, they'll need strong teeth.

According to the Grand Robert french dictionary, "coutellerie" are sharp objects, made for cutting. Examples given are couteaux, lames, ciseaux, or "grosse coutellerie", haches, scies, even surgical instruments.
"Coutellerie" is also the name for a factory that makes such object or a shop that sells them.
"un couvert", on the other hand, is everything you need on the table to have a meal, including les assiettes, les verres, les serviettes, les fourchettes, les cuillers, les couteaux.
When making a restaurant reservation in France, it is common to ask for "deux couverts" rather than asking for a table for two.

it is la coutellerie but I would still like to know why de la coutellerie cannot be used - anyone?

It works as a sentence but in this sentence they want des meaning cutlery and not les meaning the cutlery.

posséder means to own or possess. Not exactly the same thing. You can have something without owning it, and you can own something without having it with you.

Pour + infinitif means in order to. Pour manger = to eat, for eating.

Because it has to be the verb to eat

because you used the wrong words https://dictionary.cambridge.org/dictionary/english-french/cutlery