probability distributions – Why can’t you find pdf of Y by subbing into pdf of X?

If given the pdf of X, f(x) and that X = 2Y why is necessary to find the cdf of X then the cdf of Y which you then differentiate to find the pdf of Y? Since X = 2Y isn’t it true that x = 2y as well i.e. a given value of x must be twice the value of the corresponding y value? In that cause you would just sub x = 2y into the pdf of X to find the pdf of Y which is clearly not the case. I can’t seem to understand this notation as if X = 2Y doesn’t that mean x = 2y? Could someone please explain why this is not the case?