It is being written by an 8 year old.

As others pointed out, that phrase clearly wasn't.

This discussion is off topic.

This is an argument to be proven, not a declaration to be made.

It's sort of one of those meaningless inspiring self-esteem phrases that don't actually make much literal sense but people say anyway and have an ounce of truth behind them.

It's either "meaningless" or it has an "ounce of truth". Which is it?

It's sort of like when people say "my culture is a gift to this country"

Except that it isn't. If your culture is a gift to the country, you'd logically want to learn about it and educate others concerning it. Culture exists independent of the individual, not inherent to them. If you're a "great gift" simply by existing as a female, where do you go from there? Can you strive to be "more female"? To be more in existence? What goal is suggested by that statement?

Anyone who interprets such a sentence literally is just trying to shoot down peoples' self-pride for the sake of starting an argument,

You say this like it's a bad thing. Humans already have a tendency to be rather self-absorbed and conceited, traits which are actively encouraged by consumerist culture to sell product (fun game; count how many ads you see that tell you you "deserve" something or that you're "worth it". Amusingly, they never seem to admit the obvious counter-argument; if I'm "worth it" and I "deserve it", surely you're not going to make me pay for whatever it is?). We seem to be surrounded by a culture that promotes and is plagued by such undeserved pride. I deserve fame for no real talent. I deserve a huge house I can't afford. I deserve an outrageous bonus for a comparatively unexceptional amount of work. I deserve to skirt the rules and laws of "normal" society, because I'm inherently special, and that specialness is meaningless if it isn't recognized via exceptional treatment.

Girls even from a young age, or really any individual, can feel undermined or negative about themselves and/or their gender

Sure. But why simply take the knee-jerk opposite reaction to someone being made to feel bad about ascribed characteristics by making them feel good about said traits? Why not transcend the issue altogether? Why not say, "It's not "good" or "bad" that you were born a certain way; it just is. Let's focus on giving you ways to feel good about yourself in areas you can control"?

saying a self-pride statement like this is positive. It's not that intellectual or technically correct, but it sure isn't entitled.

It's really the definition of "entitled", because it accords pride to the individual for traits they possess purely by chance. Demanding something you had no hand in earning is pretty much what "entitled" means. Instilling a sense of pride in kids is great, but why not make it pride in things they do, rather than things they are? Interestingly, that seems to be more-or-less what the little girl did here; she talked about all the great things girls can do, rather than what's great about girls just because they are girls.