I'm assuming that your question is: Why should we be so privileged? What's with the exclusivity? Well, first we've gotta establish: what are the implications of being part of the "Chosen People?" For this, we have to define the word: Israel. Israel is typically associated with the Nation of Israel, or the Land of Israel, but, actually, Israel is a concept, and those two examples (the nation and the land) are expressions of the concept. They are manifestations of Israel, they are not the essence of Israel.
OK. So what is the "Concept of Israel?" I'd say that a good starting definition is: 'Israel' is the vehicle, or the method through which the Almighty fulfills His purpose in this-here world that He created.
Working with this definition, the idea that 'Israel' should have expression in a particular group of people means that the said group of people is going to be central in the process of the Almighty's fulfilling His purpose in the world.
So far so good?
Next: Why should one group be chosen over another? It is really more a matter of choosing, rather than being chosen. By this I mean: The group that was willing to accept the responsibilities involved in being the Nation that plays this role in the Creator's master plan, gets chosen.
But, better yet: Why shouldn't it be that whoever wants to be a part of that process can decide to be? The answer to that second question is: Correct! It is that way. Anyone at all can decide to be a part of that process. How? By joining up with those who have already joined up. That entails signing up for membership. Membership obviously has it's privileges, but it also entails responsibilities. So joining up means that you are ready to live by the commandments that the Almighty gave to those who elected to fill this role. But anybody who is so inclined to rise up to the challenge and privilege of being a part of the process whereby the Almighty fulfills His purpose for having given existence to existence, may do so provided that they successfully demonstrate that they are serious about accepting the duties that the role entails.
The truth is: the question is the opposite. Let me explain. According to Judaism, if you're born Jewish, which is just another way of saying: part of the Nation of Israel, then you're stuck with it. You may try to walk away from it, but we'll always consider you to be Jewish. Even if you become an enemy of the Jewish People, if and when you decide to come around, then you do NOT need to go through any conversion process. You were Jewish all along, and you still are. Not only that, but even if you never return, if you are a woman then your children are Jewish, no matter how far you stray from Judaism. And if you are a man, as long as the mother of your children is Jewish, then your kids are Jewish, no matter how vehement an enemy of Israel you have become. You can't shake it. If you're Jewish then you're stuck with it. Now, wouldn't it be more fair if you had the choice as to whether or not you wanted to be a part of this process? If you're into it, then great. But if you're not, then: "adios pardner." Why is it fair that you should be stuck with this "privilege that comes with all these responsibilities?"
The state in which a person actually has such a choice is precisely the state of a person who is not born Jewish. If he (or she) is interested in stepping up to the plate, then he may do so. If he'd prefer to pass, then he may do so.
So we now have the ironic situation where it may actually be more politically correct to be born not Jewish rather than to be born Jewish!
This is actually a very important question, but it is not the question that was asked. If the intent of your question was: the problem of exclusivity, then I would suggest that the question is answered: There is no exclusivity. Anybody may join up. And many do, by the way. Some of the greatest members of the Nation of Israel of all time were converts or the descendants of converts.
I know full well that we touched upon many issues that we didn't resolve. But whadaya think? We can address all of the side-issues in one post?
All the best