All of this is coming from a book on chaos theory I read ~5 years ago, so take it for what it's worth. As I recall:

Microscopic wind currents cause worldwide changes to the weather in about a month.

On a frictionless billiard table, extremely microscopic differences in initial conditions cause significant changes in the system after about a minute of collision, since each collision magnifies the difference between model and system results.

Plus, your claim was a claim about all systems. His claim was a claim about some systems. In general, you had the harder case to make.

Anyway, the wikipedia article was a good place to start, but probably not deep enough if these questions interest you greatly.