I'd be willing to bet that humans will stop driving cars much sooner than they stop farming. Humans have been practicing animal agriculture for a long time...
Might be some correlation there, but probably it's mostly unrelated. We did many things for a super-long time then stopped, because we found something better. For example, we used horses to get around for millennia.
We've done animal agriculture for a long time, but once something better comes around, we'll switch - and food technology is getting very close, and has other benefits too (helps against global warming, etc.).
But just like riding horses, eating animal products will never go away completely, of course.
This mode of (purely statistical) longevity argument is the "Doomsday Argument". The classic version is about predicting how much longer human civilization might endure. The crux of it is that there's only a 5% chance that we're currently in the first 5% of humanity's total timeline, and a 95% chance that we're in the last 95% of it.
If we assume that 60 billion humans have been born so far, it can be estimated that there is a 95% chance that the total number of humans ever will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1,140 billion humans will be born in 9,120 years.