To turn away from something such as a method or an idea means to stop using it or to become different from it. Japanese corporations have been turning away from production and have diverted into finance and real estate
refuse entrance or membership; "They turned away hundreds of fans"; "Black people were often rejected by country clubs"
If you turn someone away, you do not allow them to enter your country, home, or other place. Turning refugees away would be an inhumane action Hard times are forcing community colleges to turn away students