Okay, first up, you were being asked to only discuss 2 opinions in this essay, the pro and the con. Why did I read a personal opinion in there? It was not asked for and therefore, is not a necessary part of the essay. You unnecessarily extended the essay content when it should have simply been straight to the point and discussed from a bystander's point of view. The decision as to whether the media should be allowed to publish private information about celebrities should have been left as an open ended question that the readers could have decided for themselves based upon the discussion of the two differing points. It is because of that deviation, and some simple grammar errors that I will grade this essay a 7 out of 9. Now, to correct the grammar mistakes :-)
Almost everybody is interested in celebrities' personal lives. People have an unquenchable thirst for knowing about their favourite singers' lives, as an example, where they live, with whom they have relationships, and the like.
- According to formal grammar use rules it is acceptable to use an apostrophe without an S to show ownership when the name ends with an S. So the method by which you used the apostrophe in this instance is in error since you used the apostrophe to create a plural form for a word or ownership in a word that is already in plural form.
- ...
for example, where they live...
However, when we see the confrontation of famous people with correspondents who are trying to cover their private lives' news , we will find that all of them are completely uncomfortable with this situation.
gays' rights
You really are going apostrophe S happy in this essay :-) You will need to revise that due to the grammar rules I quoted above from grammarbook.com
On the other hand, we should not forget that people with newsworthy lives are human beings and they need privacy.
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We should not forget...
Nobody would feel he is at his home if a pair of eyes, named as the media
- ...
known as the...
In my opinion, privacy brings us security. When we know that there is a place that nobody else has an access to, it pleases us and puts us in rest mentally. I believe that prominent people who are at the center of attentions deserve to experience this feeling too, since after all we are humans.
- This isn't really needed in this essay. Your opinion is not being asked for.