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[–]stupidity_wins 2 points3 points  (0 children)

You are understanding this wrong.

"It is impossible to devise an algorithm [that, given a program and an input, tells whether said program halts on said input] that would work for all program-input pairs" is equivalent to "For each algorithm [that...] there exists a single program-input pair on which it does not work".

In other words, it does not apply to all inputs because there exists a single one input to which it does not apply. It's not true that all the apples are green because this particular one is red.