[JKCalhoun]

Your example seems to miss the point.

Of course I look both ways but I still cross the street.

I've watched people (friends included) who have let fear so overcome them that they frankly miss out on life. Won't travel, nervous about even leaving their home…

[BuckRogers]

Looking both ways is letting fear dictate your life, at least enough that it changes your behavior in major ways. Fear is an important component of staying alive. Fear not dictating your life means not looking and expecting everyone to stop for you.