Based on the passage by Frederick Douglass and the use of the word "rush", we can say the following as the reason why Douglass uses it:
It connotes an extreme version of hurrying.
Connotation is the meaning of a word inside a certain context. That is, since the context can be used to lend emotional weight to a word, its meaning can take on different nuances.
In the passage by Douglass we are analyzing here, the word "rush" is used to connote an extreme version of hurrying. The person did not move toward him just quickly. It was quickly and with certain violence, as if in a lot of hurry to snatch the newspaper from him.
Learn more about connotation here:
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