Because that's pretty much what he says in his post to comp.compression, where he announces that someone accepted the challenge. Let me quote:

> Before naming the individual and giving additional details of our > correspondence, I would like to give him some time to analyze the > data I will be sending him. It would be very easy to point out to > him the impossibility of his task, but far more interesting to see > how long he will struggle with the problem before realizing it for > himself. > > I am supposing that one of his fellow co-workers probably referred > him to my challenge, as I cannot fathom that someone would read the > comp.compression faq first and then want to participate after > understanding the futility of the effort. On the other hand, some > people just don't understand information theory too well. > > I'll try to give him a complete explanation of his error after a > week or so, I guess. :)

So Mike is just smug about how clever he is, how stupid the other person is, not even suspecting there might be a loophole in the challenge.

I see no sign of interest in learning what the other person is up to, or even admitting that there might be something to learn.

Because information theory says it's impossible.

I would say the update he posted to the news group rules this out.

There was a problem in comp.compression (or whatever Usenet newsgroup) of arrogant challengers announcing their brilliant new compression algorithm. This bet is a way of demonstrating at least the pigeon hole problem to other people.