Often a bitcoiner will say "1 btc = 1 btc" and then someone, thinking they are clever, will respond with "well 1 usd = 1 usd" - so I'd like to explain the flaw in this response, and I'll use a simple example to do so.
Let's take some constant, like "1 meter." The "meter" is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.
Since the speed of light does not change, the length light travels in that time in a vacuum does not change. Therefore, the meter is an unchanging and permanently fixed constant backed by physics and mathematics, i.e. "1 meter = 1 meter."
If the speed of light were somehow centrally planned and constantly changing (read: inflating), then 1 meter would not be a reliable and we could not measure length effectively. Buildings could not be built and no one would be able to communicate distance. You can substitute the meter with any other mathematical constant to illustrate the same concept.
Similarly, a "bitcoin" can be defined as a single token out of 21 million. Since the cap cannot change, a bitcoin is also a permanently fixed constant backed by physics and cryptography, i.e. "1 btc = 1 btc."
The same cannot be said of the dollar, as it is one unit out of a forever increasing total, centrally planned supply. This is similar to the speed of light always changing, messing with the "meter" definition and our ability to measure. The changing inconsistency of the dollar leads to distortion in "measurements" (read: prices) that is destructive to society - which bitcoin remedies.
It is the first constant in the field of economics. The importance of this can hardly be overstated.
tl;dr: The "1 btc = 1 btc" does NOT mean how much a btc is valued in fiat, nor does it indicate how much a bitcoin can buy, nor is it a tongue-in-cheek tautology. It's a phrase indicating the fixed, mathematical, physically-tethered nature of bitcoin.
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