The main problem that the scheming Ellsworth Toohey has with Howard Roarke is that Roark doesn't care one wit about what other people think about him. Roark believes in himself, he knows himself to be creative, genius and singularly focused and hard-working, and all of those values go against the mantra that Ellsworth Toohey is trying to spread through society. Toohey is preaching putting yourself before others at the expense of your own talents. He is preaching that individualism is evil, that success is evil, and that conformity and collectivism are the only moral ways to live. Roark defies all of those "morals": he refuses to conform, he refuses to not live up to his own personal vision, he refuses to care what others think of him, and as a result, doesn't ever do what the majority thinks is right, but what he thinks is right. Roark stands as a beacon of self-worth, strength and confidence in mankind, and how it's okay to love your own mind. Toohey teaches that you must submit your mind and all of its logic and genius to the humbling influence of letting others get ahead in order to have their chance at success too; unfortunately, Roark doesn't buy into that philosophy, and so threatens to bring down Toohey's success as a powerful influence on society's mindframe.
If Roark falls, that means that Roark, and his belief in the human mind as capable of amazing and beautiful things if let alone to succeed, are wrong, and that Toohey is right. As long as there are people like Roark out there in the world, then Toohey cannot have complete and total submission to his collectivist worldview. Roark is a threat, he's a wild card, he can't be controlled, his mind can't be molded, and so Toohey must bring him down to succeed in his own devious schemes.
I hope that helps clears it up for you a bit; good luck!