'Expensive' and 'cheap' are both adjectives,.which means you can simply use these antonyms and rewrite the sentence 'this is not cheap' as 'this is expensive' and keep the meaning the same. 'Without' here is a word connecting the clauses together. and not an adjective. You have given a statement 'You may not talk to anyone who is not a friend of ours', and then qualified it with a condition, 'without my consent'. You can't use the antonym 'with' because it doesn't make sense because you need 'the connecting word to agree with the first part of the sentence. You would have to say 'You may talk to anyone who is not a friend of ours, with my consent.' But the meaning of this is different to the original sentence. Instead you could rewrite it instead as something like 'You may not talk to anyone who is not a friend of us unless you have my consent.' But 'unless' isn't an antonym for 'without'.

When you are changing sentences from negative to positive or vice versa, you often have to think at the phrase level rather than the word level i.e. look for opposite paraphrases rather than direct antonyms. For example 'without my consent' means 'if you don't have my consent'. So one way of losing the negative is to rephrase this as '....unless you have my consent.'

What's wrong with "with"?

Ok, what I am trying to understand is this. if " you may not talk to anyone who is not a friend of us/for us without my consent, then consent is not required if it is to a friend of us, right?