The fact that "the set of 'all Countable Things' is unCountable" , is , ultimately , no more surprising that the fact that "the set of 'all Finite Things' is inFinite" .
If you start counting one number at a time .... 1 , 2 , 3 .... you'll never count all the numbers, given the fact that , one day , you'll die . We'll all die, eventually . There are some things that you cannot count even if you do live forever . The trick is understanding and learning to live with your limits.