I have a custom of 'catching' since my childhood. When I started to walk, I liked chasing the shadow of street lamps. When I joined school, I quested for winning every competition. Every time I came back home with a new certificate, my father always kidded that 'little eagle had caught a prey again.'
^Chasing, and questing, is not 'catching'.
This metaphor was too ruthless and casual because it seemed as if I was an eagle who just swooped down on its prey without any effort. My father neglected all the efforts I had paid to win.
^Ruthless and casual? An oxymoron or juxtaposition. However, not that effective because I do not understand it. Also, eagles do swoop on their prey with effort. They calculate, watch, observe, and strike. Also, you mention that he was kidding. Now, you say that he 'neglected', which kind of gives a different impression.
*Your fourth paragraph needs heavy grammar revision.
Woah, woah
'couldn't accept my failure and reminded of those days I had struggled. I didn't attend my grandmother's seventieth birthday but studied alone at home, I gave up the chance of travelling with my family to Sweden but flung myself in supplement materials, I missed the opportunity of meeting my childhood friend but locked myself in the library. All I wanted was to win. My father would never understand the happiness I had sacrificed to win, the efforts I paid to excel others. Perhaps this time he would ridicule me that 'the little eagle failed to catch its prey.' I dashed my tears with the back of my hand just liked an eagle lipped its own wounds.
My father had already gone to work like nothing happened next morning. My hypothesis that he didn't care me was deeply confirmed. But when I sat in front of the table to have my breakfast, a note under my coffee cup with my father's handwriting came into my view
^From the moment you lost and sat in your room alone, to the next morning, you did not go to your grandma's birthday and did not go on a family holiday to Sweden. All of these events, took place in the space of one day. If not, then I consider revising this paragraph to make it more sensible.
'I was moved. My father opened the cage for me but still stared at me silently. '
^Umm. I thought he went to work.
My memory flashed back to the past: My father never said goodbye every time he sent me to school but I still felt the warmth of his vision on my back.
^You never gave this impression before. Suddenly, you feel it?
The same applies to the rest of the paragraph. You give the impression that he is in fact a caring father, when one of your first lines of this essay says that he 'never cared'....
It's my first draft, so I think I need to spend more time to work on it!
^I think you do.