leadership makes me crazy

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well, since the summer holiday is coming, i begin to look for some internships as what most chinese university students do.but to my surprise and disappointment, i found out that almost all internships require applicants full of leadership. of course , i know leadership and teamwork spirit are quite important, but unfortunately ,due to various reasons , i did not be quite active in these student organizations. to make things worse, it seems that the only proof of leadership is you used be , say , the president of student union. i think maybe the defination of leadership is different in different country , particularly different accroding to weatern and eastern cultures. so what is your opinion? and can you give me some suggestions on my problem?