Why is a kanji written that way?

For more in depth kanji etymology you should consult the works of 白川静

But here is a quick and dirty explanation for the 教育漢字

http://www.harakin.net/education/kanji/kanji.htm

教育漢字 Elementary School Kanji

The kanji kids learn from grades 1 to 6:

http://en.wikipedia.org/wiki/Kyōiku_kanji

http://www001.upp.so-net.ne.jp/NYAO/db/kanji/