"The boy gets out of the car."
Translation:남자아이가 자동차에서 내려요.
I'm not sure, but this is how I think it works: 에서 is a particle that indicates where an action takes place. In this case you know something is happening at the car, but it doesn't necessarily means getting to or from the car; that is indicated by the word 내려요. In English you wouldn't say you're "getting out at the car", but "getting out from the car". From also indicates the direction of the action. But not in Korean.
에게서 can be used as "from", but only as an indirect object particle, in the meaning of receiving something from someone.