The point is that you would not even question any of this if you had never learned as a child to count the elements in a set to find out how big the set is.
If instead they had taught you from the get go that one set is as big as another if and only if there is a bijective function between the two sets, then it would be 100% natural for you to say that the set of even natural numbers is as big as the set of natural numbers, that the set of real numbers is bigger than the set of natural numbers, that the set of real numbers between 0 and 1 is as big as the set of all real numbers and that the set of points on ray A is as big as the set of points in the entire universe.
Unlearn the preconceptions and transcend yourself!
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