Why was Hawaii undermined, and its king deposed by the US supported military action?

The American businessmen who overthrew Hawaii's last monarch did so because they could. They saw an opportunity to steal money and seize power, and they took it - there was no greater, more noble justification. Americans of that time had little respect for non-European powers, and no respect at all for the rights of smaller non-Western nations to remain free. They saw Hawaii as something they could simply steal with no shame, and so they did.