Earlier quoted context omitted.
That depends on how noisy or smooth the changes are. That's why it's valuable to look at both.
It may be - but to the above poster's point - if gas went up 20% in Jan of this year and then stays flat... is it helpful to think of prices as "going up" ? It seems misleading.
Here you are encountering a common human cognitive failing, which is the belief that there is some sort of objective answer to the question "are prices going up?" that we should all be able to totally agree on, somehow floating in Platonic space without reference to any particular measure of "prices increasing".
The problem is that if you drill down to the question of "what does it mean for prices to be 'going up'?", you must admit to the fact that there are multiple valid definitions of that. It just isn't possible or plausible to create one true definition.
In the presence of that fact, it becomes inevitable that there will be senses in which the price is going up, and senses in which they are not, and senses in which prices are going up more than other senses. That is the reality, which is complicated.
(One propaganda technique is to take one of these numbers, which really exists and is perfectly defensible on its own terms, and then use it in a context in which you know people are generally going to interpret it as one of the other senses of the term. Excitingly, by controlling which "sense" you anchor your listeners to, both "sides" of a debate can push the numbers in whatever direction favors them at the same time.)
According to our nationally-used, generally-accepted metric, if gas is the same price today as it was 365 days ago, inflation is zero. But does that mean the metaphorical person on the street is "lying" if they say prices are generally going up because gas is 20% more expensive than it was three hundred and sixty six days ago? There is a fundamental arbitrariness both to our metrics, and how we all feel about things. I've seen plenty of "How can annual inflation be %8 if my eggs are 2.5x more expensive than this time last year?" posts around lately. The literal answer to that question is obvious, but if someone's expenses involve more eggs than mine, either because their food is a bigger percentage of their home budget or they are a business for whom eggs is a major input cost, they may feel a higher level of inflation than I do, and they're not wrong. They've just got their own inflation metric that disagrees with the national one, but their own metric may well be more relevant to their life than the national one is.