I'm new of computer vision concepts and I'd like to know why, when we double the size of an image, we should use bilinear interpolation where pixels haven't values instead of average between nearest known values pixels.
I'm not sure I agree with the premise that you "should use bilinear interpolation". You shouldn't blindly use anything without thinking about it. For example, if your pixels represent the result of a classification and 1 represents wheat, and 2 represents water, and 3 represents barley, you certainly shouldn't take the average and assume that when you enlarge an image of wheat and barley that some ocean suddenly appears in the middle between the fields.
Bilinear interpolation is actually just averaging, except a) it is in 2 dimensions because images are inherently 2-dimensional and b) if you know you are nearer to one point than another, surely it isn't unreasonable to weight your "guesstimated" value (which, after all, you don't actually know) more towards the geometrically closer value?
I guess my answer is really that there are several types of interpolation, and you should apply some thinking to deciding which one is best for your particular circumstances. Sometimes you don't want to introduce new colours because of classification or palette issues, and in these circumstances you need "nearest neighbour". Sometimes "bilinear" is what you need, sometimes "bicubic".