You'd have to be driving 18.3% the speed of light for a red light to appear green. I don't think the officer is buying your "I wasn't going that fast."

I agree. That's what I meant by "change over time within A/B." If the purpose of a graph is to show whether dogs or cats are preferred, then there should be a single % of households containing [pet] axis so the magnitude of the values can be directly compared. Whereas if the purpose is to show the effect of the 2008 recession on pet ownership, it may be more appropriate to have two separate axes so the magnitude of the change in values can be compared.

If the units are different, then you can't plot the two series with only one vertical axis and so of course two different axes is ok.

But this example is in percent, so the units are not different. If the purpose is to compare the magnitude of series A to the magnitude of series B, then they should use the same axis. Using different axes would be acceptable if the purpose were to compare change over time (or whatever horizontal axis is) within A to change over time within B (as you might with, say, % of state budget spent on education vs % graduation rate). In this case, it's useful to zoom in on each series independently so the change over time is maximized.

2 has this problem as well, just on the horizontal axis.

If the body identifies toxic food while it's in the stomach, the most efficient route out is back out the way it came in, i.e. vomiting. Once it passes into the intestines, though, then you're right that the best way out is forward (quickly).