The phrase "considerable controversy" means that there is a lot of disagreement or argumentation regarding a particular topic or issue. Full definition
The question of whether runners should stretch before or after running or even stretch at all has generated considerable controversy. (MomsTeam.com)
«This proposal has been a matter of considerable controversy,» writes the author of a 1980 article on a type of bacteria. (edutopia.org)
There is considerable controversy over which form of psychotherapy is most effective, and more specifically, which types of therapy are optimal for treating which sorts of problems. (psychology.wikia.com)