In his first two appearances, Brunt is the antagonistic representative of the Ferengi Commerce Authority (FCA). The first few times we see him:
- He investigates Quark's mother for doing business & earning profit.
- He investigates Quark's bar and the 'rumors' of the worker strike and unionisation.
Although his demeanour could be considered stuck up/deliberately antagonistic, in these cases he's really just doing his job as an agent of the FCA.
But then the next time we see him, he's deliberately going out of his way to destroy Quark: he takes great pleasure in shutting him down - revoking his business license for breaking a contract to buy Quark's remains, which he had planned to desecrate... for some reason.
Memory Alpha's description on Brunt only had this to say:
After these two encounters with Quark, Brunt grew to hate him.
Why does Brunt despise Quark? I mean, he's a slimy businessman sure, but why the open hatred? Why is disgracing Quark's remains worth 500 bars of latinum to him? Is it only because he's managed to wriggle out of the FCA's grasp more than once or is there something else going on?