‘I want to meet your enemy’ can mean?:
- You are not an enemy
- You are an enemy (like ‘your majesty’ means you are a majesty)
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'I want to meet your enemy' is not ambiguous, and means only one thing:
I want to meet the person who is your enemy.
'Your' denotes possession or association. It is like saying 'I want to meet your wife, brother, son, boss, neighbour, etc'
The word 'your' in formal or respectful forms of address used when speaking to people, such as 'your Majesty' (to the British monarch), 'your Honour' (to a judge in court), 'your Excellency' (certain senior officials or politicians of foreign states) does not mean 'you are'. It is possessive and conveys the idea that majesty, honour, excellency, etc, belong to that person. When talking about (rather than to) such people formally we would say 'her (or his) Majesty, Honour, Excellency'.
Titles or "styles" such as "Your Majesty", "Your Grace", "Your Highness" are named after abstract qualities.
"Enemy" is a concrete noun. There is no way that "Your Enemy" could be a title. It is just about conceivable that in jest something like "Your Hostility" or "Your Enmity" could be used as a title or form of address (perhaps "Your Odiousness" would work better) - but surely not "Your Enemy".
So "your enemy" isn't ambiguous.
One thing from the original question that has not yet been mentioned in an answer:
- You are not an enemy
It doesn't mean this. Requesting "I want to meet your enemy" says nothing about whether you are my enemy. It's possible that you are my enemy and the person I want to meet is your enemy. It's even possible that everybody concerned considers each of the others to be an enemy.
In itself and without context, the phrase is not ambiguous. The direct meaning is
"You have an enemy. I want to meet them."
However, adding cultural knowledge to the context, this phrase can deliver a lot of subtext. Take the old adage "The enemy of my enemy is my friend" as context. If the speaker of the phrase speaks in this context, the phrase could mean
"You are my enemy. If you've got another enemy, I want to meet them, so I can team up with them against you."
On the other hand, depending on context, it could also mean
"You are my friend and I want to protect you. I want to meet your enemy, so I can destroy them."
You are an enemy (like ‘your majesty’ means you are a majesty)
There's a semantic difference between the use of possessive pronounces here, for which I would bet some languages make a grammatical distinction as well.
Your Majesty implies you possess the attribute of, or the quality of, "majesty". Because and only because you are a majesty if you have the "majesty" attribute, it follows that you are a majesty.
But if the possessed noun is not an attribute or quality, this relation does not hold.
Referring to "your leg" may imply that you have a leg. But obviously having a leg does not mean you are a leg.