[beowulfey]

It is a comparison of two averages, not of a single temperature to an average. A changing average suggests a change in the underlying factors at play, because while a single observation may not ever match the average as you say, a system in equilibrium should not see the average changing. This is why it is called anomalous: the mean is changing continuously.

It’s a crude metric but in the framework of the analysis (pre-industrial vs post-industrial) it is an appropriate comparison.

[PeterisP]

I would consider that "anomaly" would refer to something unusual or unexpected, an outlier, or a weird unexplained occurrence contrary to our expectations, or a one-off deviation followed by a return to the norm.

On the other hand, a continuously changing mean or a systematic pattern IMHO is not an "anomaly"; something can't be unusual for long - if something has become or is clearly going to become usual, then it's a "new normal", it's a "trend" or something like that, but not an anomaly anymore; if we're seeing what we expected to see, that can't be called an "anomaly" because that's the expected result.

With respect to climate change we see that the underlying factors have changed, we mostly know why, we observe the consequences now, see their trends and can predict how the mean is going to change - so all the factors are contrary to the definition of "anomaly".

[beowulfey]

Yes, this is a good point. It is only anomalous if we expect the mean temp to remain relatively constant—it is definitely dependent on the conceptual framework!

[kkjjkgjjgg]

I don't think that explanation is correct. The average temperature of a year is just a specific way to take a measurement. Comparing it to an average of averages over several years is then the same as comparing a measurement to an average of measurements.

That the climate should never see averages changing seems obviously false. There clearly are cycles that last longer than a year, for example, as several ice ages came and went before industrialization. El Nino take phases last between two and seven years.

[beowulfey]

Yes, the averages can and do change—that is my point. A changing average suggests something about the system is changing. It doesn’t need to be compared to preindustrial temperatures, but it is a good baseline because the temperature variation (as shown in the chart) was pretty small within that timeframe compared to the changes we are seeing today.