From Hal Daume's blog:

If you believe A => B, then you have to ask yourself: which do I believe more? A, or not B?

Let's say a weak compressor is one that always reduces a (non-empty) file's size by one bit. A strong compressor is one that cuts the file down to one bit. I can easily prove to you that if you give me a weak compressor, I can turn it into a strong compressor by running it N-1 times on files of size N. Trivial, right? But what do you conclude from this? You're certainly not happy, I don't think. For what I've proved really is that weak compressors don't exist, not that strong compressors do. That is, you believe so strongly that a strong compressor is impossible, that you must conclude from (weak) => (strong) that (weak) cannot possibly exist.