Sort of a complicated question, I'll try to ask. How was I born me and not another?

[EruptedCarcassBloat]

And by the way I think I figured out a different way of simplifying the question. You know, a lot of people say that you were one lucky sperm out of a ton of sperm that didn't make it. You could have just as easily been the egg, which would make it a lot easier to imagine the possibility of you being born.

All of us, in that sense, are both the egg and the sperm.

GIGO.

However, what is the possibility of the egg giving birth to you?

-again, 100%, it's an event known to have occurred, as inaccurately as you've framed it.

It's strange because there's all these people around me who are not me they were all born from an egg too.

But not the -same- egg, hence, "them"....vs "you".

If, goodness forbid, my mom died before I was born, then I would have essentially never existed.

Correct....finally, lol.  

This is one way to look at it, but then you have to wonder, there must have been other factors that determine whether or not a person was born. A woman goes through her period producing a different egg every month. So that seems like it further slims the chance of you actually being born,

Everyone born from every egg is "me" or "I" to them.

not to mention the fact that every time there's a new egg, there's a new child that could be born, all the children from a mother are different unless they're identical twins. This seems to make me think that the possibility of being born is actually very slim.

The chances of conception relative to intercourse are pretty low for any given "you" "I" "me" or "them"...and yet the world is full of all of the above.  Thankfully, even when the chance of something happening is low in any specific instance, the presence of billions of such instances playing out all day every day (people love to bump uglies) make an individual improbability a collective inevitability.

All that sex means that someone is going to be born...you are just such a someone, and in that, you're not improbable at all.  In fact, I bet you were expected.

But isn't it just the same probability of a single droplet of rain landing on someone's face?