"To dominate the discussion" means to have a lot of control or influence over a conversation or debate, often by speaking more than others or by having strong arguments that others cannot easily challenge. Full definition
But it would be unfortunate if it led to still greater separation between physical and social scientists, with economists dominating the discussion of policy options even more than now. (judithcurry.com)
On social media, the matter is still dominating discussions on various social media platforms. (ghanapoliticsonline.com)
The debate over the use of armed drones continues to dominate discussions about the future of war. (heritage.org)