In a statement they said, "Michelin considers Formula One to be a highly technical motorsport in which the tyre is a very influential component in the scope of the performance of the vehicle. The teams' freedom to choose their own tyres is essential. Therefore, competition between at least two tyre manufacturers is critical; this provides the basis for real competition between tyre suppliers, which, in turn, stimulates progress for the public's greater interest. Today, it would appear as though Formula One rules will be modified to impose a single tyre supplier. After consulting with its loyal partners (McLaren Mercedes, BMW Sauber F1, Renault F1, Honda Racing F1) as well as with Sir Frank Williams, Michelin is now convinced that the evolution towards a single tyre supplier is inevitable. Michelin expresses its regret to see F1 lose a part of its high technology."

The statement also revealed the true extent of the frustration between Michelin and the governing bodies of the sport in regards to the constant changes that are made to the rules.

"In addition to this new direction in F1, there are constant changes to racing regulations without warning. Such practices also make planning for the future completely impossible. In this context, continuing to make long-term investments in Formula One no longer presents the same interest. Michelin has therefore decided not to extend its Formula One involvement beyond the 2006 season. This decision is the result of profound differences between Michelin's long-standing sporting philosophy and the way Formula One is managed by the regulating authorities, which no longer provide a clear and sustainable environment to justify long-term investments," commented Mr. Edouard Michelin.

They did say however that if “F1’s ways of functioning were to be significantly modified" they would have no hesitation in returning.
It is incredibly unlikely that that will happen in the foreseeable future so it now looks almost certain that F1 will have a single tyre supplier in 2007.