Pretty much what has already been said. What we define as "normal" is just a culmination of what society and culture says is as such--a social construct. What can be considered "normal" in your culture could be considered as not or even taboo in another culture. Society may say it's normal to go out and be rebellious as a teenager, but is it really "normal"? Is it really not "normal" to not like a certain music, genre, style, form, etc.?
I don't think normality
really exists: we might think there is, because we've grown up with a set roster of standards we should adhere to; however, is it normal because it's natural, commonplace, or "common sense," or is it because people say it is? Normality changes as time progresses: it was considered not normal to have tattoos decades back (for several reasons), but now, less people make a fuss about it because it has become more accepted and viewed as "normal." (there are a lot of better examples I can't think of for some reason, so don't mind me if I came up with a bad one)
I think people attempt to be "normal" by adhering to social standards. Some people do certain activities because it's "normal" for their age group, gender, ethnicity, nationality, etc. and fear being ostracised for diverging from the social standard, because what they're doing isn't typical. I know some people would think I was weird because I didn't do "normal" things like going outside to have fun, or wear certain clothes because it's "normal" for my age, or like certain foods because of my ethnicity. Some people who don't act "normal," as defined by
social norms, may be considered deviants of society, and are therefore pushed to become normal by others.
Maybe we lose a lot of great ideas and remarkable people, because we push them to be "normal."