Anbuhl grew up in Eckernförde in northern Germany. He graduated with a degree in teaching from Christian-Albrechts-University in Kiel.

From 2003 to 2008, he headed the Parliamentary Liaison Office of the German Education Union (GEW) in Berlin. In his last position, which he held from 2009 to 2021 he was Head of the Education Policy and Educational Work Department of the German Trade Union Confederation (DGB). Anbuhl is an expert in all areas of the education system, from early childhood education to higher education and vocational training.