What's the Deal with Peak Oil?

Having come across the term "peak oil" quite a bit in recent months, I've decided to poke around the internet a little in an attempt to reduce my ignorance about what's behind the phrase. The denotation of the term is clear enough, of course: It refers to that moment in history at which the extraction of oil from the earth is at its maximum. But there's more to it. That is, there is a noteworthy number of individuals and organizations that think this is a problem that should be a focus of everyone's awareness and of politics. Insofar as it is legitimate to summarize the standpoint of various individuals and groups based on limited research, the peak oil activists' position seems to boil down to the following:

1. We are at or near peak oil, which means that in the near future the same amount of oil will not be available at the same prices, and sooner or later it's going to be used up.

2. Therefore, we must change our way of living now: sustanable cities, less use of cars, local production, etc.

But there seems to be a huge disconnect there. If it is indeed true that in the near future the same amount of oil will not be available at the same prices, then the problem solves itself: Raising prices will cause changes in lifestyles. For example, the more expensive petrol is, the more motivated you are to take the bike rather than the car. Also, the higher the price of petrol, the more companies are motivated to offer machinery that uses alternative sources of energy.

As a consequence, if the empirical assumption is true, then there is no need whatsoever to campaign for lifestyle changes, because they will be brought about automatically, via the price mechanism. If you see these lifestyle changes as desirable anyway, you should be quite happy about peak oil, no need to panic.

So, what am I missing?