The phrase "greatest impediment" refers to the biggest obstacle or barrier that prevents someone or something from achieving their goals or desires. Full definition
Perhaps the single greatest impediment is the dearth of talented attorneys helping school administrators find their way. (educationnext.org)
When we're young and just setting out in our careers we tend to assume that the greatest impediments to our progress and success are external to us. (entrepreneur.com)
Our nation's crumbling, aging infrastructure is now the greatest impediment to maximizing economic growth and prosperity. (businessroundtable.org)