Why is deflation not considered the opposite of inflation? In this article from 2013 on bitcoin, the author casually states the importance of knowing that "deflation is not the opposite of inflation", without expanding or elaborating. I'm sure that there are differing points of view, but can anyone provide support for this statement and its importance?

To me it seems that deflation is a decline in prices, while inflation is an increase in prices - making them opposites. However, I'm guessing that the author is referring the effects of inflation and deflation not being opposite, or perhaps there are some differences when considering pure currency (the article is about bitcoin) vs. the effect of a currency in the market.
People think that inflation is bad when it gets out of control, say when its more than 3 or 4% a year. The idea is that we all make economic decisions based on prices and its harder to make those decisions when the prices are constantly changing! Moreover, we try to avoid holding on to money and committing to a price for a long time, because we know those become meaningless over time. Also people associate inflation with the ills of fiat money, and other such things.

Deflation would seem to be not a big deal. You hold on to your cash, it buys more things as time passes! But, it turns out to be a big deal. Deflation turns the real interest rate paid by cash into a positive number. And that means that when the fed wants to lower rates a lot to get you to spend and borrow, it can´t lower them below that real rate. So it can't get you to spend and borrow -> economic fragility! Fed is powerless! So people are now scared to death of deflations! Even small ones seem to be hard to turn around. Japan has been flirting with deflation for a long time, unable to escape from its cold grip....

Therefore, to answer the question:
 Inflation and deflation can be defined as opposites: inflation is a positive rate of change of prices sustained over several periods while deflation is a negative rate of change of prices sustained over several periods. However, the effect of inflation and deflation on the economy are not opposites from each other, and policy-maker's concern for one and the other are different, but not the opposite of each other either.