When you mix red, blue, and green light equally you get white light, because in this case all these colours get added. But exact opposite happens in the case of paint. In paint, these colours gets subtracted to form black colour.
In simple words, when we mix paint, all the light falling on the paint gets absorbed. So, it reflects no light and gives black colour. This is because the light that doesn't get absorbed by one pigment gets absorbed by the other one. So, all the light gets absorbed.