Peak Oil is about an inflection point after which the expense of extracting oil rapidly accelerates. It's a cost issue. And those concerned with Peak Oil are afraid that acceleration will be faster than our ability to switch to alternatives, causing a period of cramping where energy jumps from being dirt cheap to tremendously expensive, until we can build out the alternatives (a process that will most certainly take decades).

There will always be oil; we just won't be extracting it after a certain point anyway. 2050 is an easy target for that.