I'm trying to reconcile these facts,

 - If I had paints of the primary colours and I mixed them together, I would produce gray. 
 - White light contains every colour. 

My most convincing attempt to answer the question: The colours of objects that don't produce light are the colours those objects don't absorb. A white object doesn't absorb any colour, a blue object absorbs all colours but blue, a green object absorbs all colours but green, etc. So by mixing paints of the primary colours I mix influences that collectively absorb all colours and reflect all colours; whereas, if I had paint that only absorbed all colours I would have black paint, and if I had paint that only reflected all colours I would have had white paint. Gray is a combination of white and gray, so I found this answer intuitively satisfying. However, I don't know if it's an accurate explanation of the observation. 

Why does mixing every paint colour produce gray instead of white?

Thank you.