greenmanHave an axe to grind

This is a very commonly used idiom meaning: to have reasons (possibly hidden) for saying or doing something. Sometimes holding a grudge against something or someone. (guardarle rencor)

 

E.g.

The pro brexit people have said that the violence is related to European tension, because they have an axe to grind-- La gente a favor del brexit (la salida del Reino Unido de Europa) dice que la violencia está relacionada con la tensión en Europa,  porque tienen razones para convencer a los demás

 

Some comments made by vegans regarding the health risks of drinking milk should be taken with a pinch of salt, because they often have an axe to grind against the dairy industry-- Algunos comentarios de veganos con respecto a los peligros de beber leche para la salud deberían cogerse con pinzas, porque muchas veces le tienen manía a la industria láctea