You are the first person I am telling this
I'm confused about your time line here. You said that when you were 16, you had that night with your friend. you However, you also say that at THAT time, had this false philosophy. But right after, you say that it didn't take long to realize that it was false, since you had that night with your friend.
So were you having the false philosophy at that night? or before, but that night made you realize that you were wrong?
obviously, it's the second one, so I'd rephrase your first paragraph a bit. (don't change the first sentence, just straighten up the time thing)
passion of what? you're writing a whole new essay here, not the old one anymore.
I become to love
I began to love
to observe...and to analyze
I become thirsty to learn more, something universal to heal peoples' hearts.
I yearned to learn something universal... learn more here is vague and could be taken out, since you're immediately explaining it
Psychology, my intended major, is a perfect match for both my interest and passion.
If you put "passion for psychology", you don't even need this sentence.
notice somebody's suffering and make him feel loved, welcomed, and worthy
you want to make sure that the reader understand that's what the poem is about. Or else you'd have to explain why you made that analogy
someday I hope to be a privileged participant in regaining peoples' pursuit of happiness
I hope to be someday
unless pursuit of happiness means feeling loved, welcomed, and worthy, I don't get why it's here. If it for some reason makes sense in your head, I'll no longer bring this to notice.
hmm...overall this is definitely a stronger essay, at least it's clearer and more understandable.
Is this long enough? I thought that these essay have to be around 500 words, in which case a minimum of 350 at least is required in my humble opinion.
If you need to add anything, I'd suggest talking more about you. In the sense that you talked plenty about your dreams/major, your friend, but not enough about the impact of the story on you.
The only impact it had seems to be that you feel helpless. But isn't it still quite a long way from feeling helpless and trying to help? Why exactly did you get inspired?