"A friend of yours?" "Well, I know the person..." Part I

So there I am, opening Facebook and am presented with many names accompanying pictures that if I think loong and haaard may invite certain recollection. The thing is that all these names/pictures have this cute li'l tab that reads Add as Friend...
Now what's a guy to do? (I'm talking about me... OK?)
Should I just click-click-click away those tabs, making these people "my friends"?

Are they "my friends"?
Am I their "friend"?

Yes, I know them. And I may know some things about them, be it their occupations or certain personality traits, but here comes those questions again: Are they my friends? and Am I theirs?
I have my own understanding of this word: friend.
I have friends, thank God, meaning that I consider them friends. But whether they consider me their friends, you gotta ask them that. I realize that I don't consider myself having many friends, and you know what? It suits me so very fine (NOT having many friends, I mean).
I choose my friends, I am teaching my kids to choose their friends very carefully. And I believe that these friends of mine, either consciously or subconsciously, "choose" to befriend me for whatever reasons.
Why am I teaching my kids to choose their friends? Because there are people out there that I strongly believe will bring harm to my kids should they become friends. I believe that NOT everyone fits to be someone else's friend. The bottom line is there are bad people out there. That is how the world is.
I can live with just a few people whom I can really call friends. And I will not befriend someone whom I think will bring me harm. I grew up being taught that one should not fall into the same hole twice, and there are qualities--good and bad--that everyone possesses; and, because of this I don't mind losing "so-called friends." (Hey, there are 6.6+ billion people in this world, what's losing a "friend" or two?)
I believe in redemption, but it is not for me to give and to prove whether a person has indeed redeemed himself.
Am I a person holding a grudge? I am a cautious person.
So, until there is another cute li'l tab that reads Add as Acquaintance, I'll stick with a few friends I have and believe.

*Fiuuh, that's a lot of F-words...*