It is amazing how effective and resilient these techniques are, if one cannot see the layers within layers. Well, it's still amazing even then.
It kind of is. That's what makes it confusing, I suppose.
If you buy a house of equal value as compared to 60 years ago, then the amount in dollars you will pay, when adjusted for inflation, will be equivalent to 60 years ago (within some margin of error; inflation is impossible to calculate perfectly). If we live exactly like they did in 1960, then inflation and the change in cost of living are the same thing.
But, people expect more today. As mentioned in several comments up-thread, take housing: They are bigger, safer, more energy efficient, more attractive, more comfortable, etc. Alongside that, the married family unit is quickly dying – people are more likely to be single nowadays, so we place more value on being able to live alone. Land is more valuable too. This is particularly noticeable anywhere near agricultural areas, where climate instability and more mouths to feed in the world has made food more valuable, making farmland more valuable, making urban sprawl out into the farmland more expensive. It goes on and on and on. So, even if the dollar was of constant value, you would unquestionably paying more for a house today as compared to in the past. But you're getting more! People are willing to pay more, in constant dollars, because it is worth it.
Only on the dollar side are you getting less. The so-called 'hidden tax'. This is what inflation tries to find. If you are a politician speaking to the people, especially on a national scale, this is the only thing in your control, the only thing that is relevant to you. People choosing to buy bigger and better things is not really of your concern. Why shouldn't someone be able to buy something nicer if they want to?
> Given that a word is defined by what the majority of the people using it mean by it
In the absence of any other definition, that is true. If a speaker defines a word, though, then that new definition takes force while they are speaking. And economists and the President have most definitely provided a specific definition for "inflation".
> I think inflation in common English is closer in meaning to COL than to the technical economics term
I'm quite sure the most common definition is "that single number they talk about on the news", which is equivalent to CPI, which is most definitely not a cost of living measure.
But in many of these discussions, it is deliberately being presented as equivalent to COL, which is never addressed separately. So, in reality, for the vast majority of people who learn about these numbers from the media, not economics degrees, "inflation" actually refers to COL, except that the numbers they are given are the ones for what economists call inflation.
Given that a word is defined by what the majority of the people using it mean by it, I think inflation in common English is closer in meaning to COL than to the technical economics term inflation.
Edit: typos