Average position lies to you most often, because it is an average smeared across every query, page, and location your site appears for, and an average can move for reasons that have nothing to do with any page you actually care about. It looks like a single, trustworthy number, so people watch the sitewide average rise or fall and draw conclusions from it. But the average is exactly where real movement goes to hide: a meaningful drop on a money query can be canceled out by a small lift on dozens of trivial ones, leaving the headline number flat while something important is breaking underneath it.
The mechanics of the deception are worth understanding. Average position is volume-weighted across a constantly shifting mix of queries, so when you suddenly appear for a flood of low-position long-tail queries, your average can get worse even though every page you optimized improved. Run the opposite case and the average can improve while your best queries quietly slip, because losing a few high-value terms barely dents an average dominated by many minor ones. It also blends devices and locations, so a regional or mobile-only change disappears into the global figure. None of this is the metric malfunctioning; it is an average behaving like an average, which is precisely why it misleads when read whole.
The other metrics are not innocent, but they are less treacherous because they are more concrete. Clicks and impressions are counts you can trust at face value, and click-through rate is honest as long as you remember it is also an average. The trap is specifically the position number presented as if it described your performance, when it describes a statistical blend. So the answer to “which lies most often” is not the cop-out that all metrics have caveats; it is that average position is the one that routinely tells you a calm story while the real picture is anything but.
The corrective is to de-average it. Never judge from the sitewide position figure; segment instead. Filter by individual query and by individual page, and read position for the terms and URLs that matter, so you see the real movement the blend was hiding. Add device and country filters when relevant. Once you read position segmented rather than aggregated, it goes from your most misleading metric to a genuinely useful one, because you are finally looking at the queries you care about instead of an average of everything.