lesson 6.9 cases

In lesson 6.9  know it test
The question asked to say in German is:  I don’t want to come along"   The answer given is: Ich möchte nicht mit kommen.

Shoulden't   the correct answer be: Ich Will nicht mit Kommen.

Which is correct? I say  ich will nicht mit kommen because  'WILL" in this case means  "WANT". if I'm wrong please explain why.
 

Technically, I think you are correct.  The use is largely a matter of emphasis.  To say 'I would like' versus saying 'I want' is a little less demanding.  It is a little more polite as in ordering a cup of coffee.