Those who opposed the provisions of the sherman antitrust act believed that success in business depended on what

 large business owners working together.

Context/history:  

The Sherman Anti-Trust Act  was the first measure by Congress to prohibit trusts. It was passed by Congress in 1890.  A trust was when  stockholders in multiple  companies transferred their stock shares to a single group of trustees. Thus a whole industry area could be dominated by a single "trust" organization, destroying the free market of business competition. This was a monopolistic practice which the Sherman Anti-Trust Act ended.  Thus the Sherman Anti-Trust Act directly went against the idea of those who believed business success should be based on large business owners colluding with one another.

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