He didn't want the competition.
Like most communist dictators, Castro made himself and his government the 'kingpin' of an international criminal organization backed by legal codes, 'authorized' force and the appearance of legitimacy. There is no greater evil than when law merges with criminality and rules a domain as though it still supports law and justice.
At least we know when the mafia is operating and can distinguish it from law and order, punishing any obvious harm or missteps it takes while seeking to 'recruit' its members into truly legitimate lifestyles. Of course, the goal of the mafia is the same as communism, corrupting all law and legal mechanisms until they are only tools in its hand and no longer a threat as competition. Left unchecked, this is what it will naturally do.
In Cuba, the mafia was being used to transition the people into legitimate capitalism from tribalism, so since the operations were contained to an island and America was already successfully assimilating many of the crime families into legitimate society on its mainland with offers of control over entire business sectors in exchange for government oversight and the end of criminal operations, it was a serious threat to communism to allow them to continue down this path. Cuba was not far away from being a free, law-abiding and prosperous island nation dedicated to capitalist ideals.
Why was it 'bad' for Castro to remove the mafia and install layers of soldiers, government agents, 'secret' police and local police forces and oppress or kill anyone in Cuba who refused to join any of these?
There was no chance of liberty or capitalism advancing in Cuba after that. He was so unyielding that his own people couldn't conduct basic commerce with anyone but other communist nations and much of that commerce was blockaded from reaching them because it required using waters controlled by the free world.
That made for great propaganda against the 'evil capitalist aggressors' but left the Cuban people living in inextricable poverty, using and creatively reusing 1950's technology while only Castro himself and his inner circle lived like royalty on illegally smuggled goods. How was that any different than the mafia, other than the hopelessness of knowing that there was no way to 'transition' to liberty or actual legitimacy or ever join the free world and advance?
Of course, they could cling to the pipe dream of communist world domination finally 'liberating' everyone, making all goods and services 'free' for everyone and all men 'equal' with no crime, suffering or evil capitalists to worry about; that is, once government controlled everything and its leaders suddenly became 'good' people.
That dream was tougher to sell the weaker communism became, especially after news leaked through the strict Cuban censorship about the fall of the Soviet Union and China's desperate need to begin opening up to capitalist nations just to keep from following the Soviets.