You know one of my favorite things about parenting? And, for the record before we begin, I'm not being snarky.
It's that you can be utterly proud and heart-warmed by something you KNOW is not just worthy of your huge response. OR that if one of your friends went on and on about that same sort of thing (and they will) your first urge (before you remember) is to roll your eyes.
But it doesn't matter. At all. Because we're not talking about thinking here. This is pure emotion.
When that kid first smiles or poops in a potty or writes a cool story on his or her own, your heart will swell with so much proud love, you almost topple over--all that, even when you know that this is something just about every person goes through. It's just such a cool thing about being human. Or maybe it's not just part of being a person. Maybe tiger mothers, watching their young pounce on bugs, just like tiger cubs have done since the beginning of time, have that same incredible surge of "isn't that amazing? isn't she wonderful?!"
And the nice thing? It doesn't go away. Sure it cools down, especially once they hit rebellion head-on. It would have to once that initial baby love stage is over, or you'd never get on with life as more than a drooling love-enslaved moron -- and your children will grow up to be horrible people. But it hangs around and gives you a jolt now and then. A little fix of pure, overwhelming love.