I see what you mean and I agree with your intention, but the wording is confusing. Remember that a set has no structure beyond containing particular elements. Consequently consider (rather simplistically) that a house and a pile of bricks might comprise the same set of bricks, but that does not mean that the pile of bricks is a house, nor that one could not make very different houses from the same set of bricks.

Similarly, a line is more than just the set of points; those points have particular interrelationships, or there is no line.

Certainly, as I assume you meant, we cannot construct a line point by point, nor see it if we could, whereas there is no point on a line that does not in principle have its own identity as a mathematical concept (though that is far from true in any physical sense).