In a nutshell, anarchism is against all types of coercion, and capitalism is coercitive by nature - but this concept seems difficult to grasp in a country which is precisely founded on capitalism (the USA) and calls itself "the land of the free". Still, there is some US libertarian who understands what anarchism really means (Noam Chomsky for example), but they usually need to label themselves "libertarian socialist" because otherwise they would be confused among the vast majority of US pro-capitalism "libertarians".
This is nonsense - how is capitalism coercive?
In very basic terms: Coercive hierarchical structures are inherent to capitalism. Individuals who do not own any means of production are forced to sell their labor as a condition for survival to those who do own means of production, triggering a "wage slavery" mechanism. You need to employ your time as your employer wants, otherwise you might starve.
As a side note, capitalism is based on a competitivity principle which is opposed to the "mutual aid" principle professed by anarchists (Kropotkin).
To make a long story short, anarchist thinkers share Marx's view on capitalism, and about this specific (coercion) point:
Alienation is the estrangement of people from their humanity, which is a systematic result of capitalism. Under capitalism, the fruits of production belong to the employers, who expropriate the surplus created by others and control what they do during their worktime, and so generate alienated labourers. In Marx's view, alienation is an objective characterization of the worker's situation in capitalism – his or her self-awareness of this condition is not prerequisite.