The main idea of this extract is that in trying to become somebody - someone prominent, someone famous, we're all becoming the same. We are conforming to the standards set by the society, and are in constant competition to become the best. But we don't realize that by doing so, we're just like everyone else. We're losing our identity and therefore, becoming a nobody.
Emily Dickinson writes in her poem, that by becoming a somebody we're making ourselves more like the public. The admiration that we seek would eventually bog us down, weigh us down, and that would ultimately lead to our downfall.
So, in order to truly become somebody, we need to temporarily leave this race, and become the best versions of our own selves.