The problem appears the moment you pour for someone else
One vessel, two cups, and the second is visibly darker and noticeably heavier than the first. It is not imagination, it is not an uneven hand, and it does not go away with practice. The liquor in a brewing vessel is not uniform: concentration is highest near the leaf bed and towards the bottom, and the liquid that leaves last has also been in contact longest. Pour three or four cups in sequence and the gradient across them is substantial — easily enough that two people can disagree in good faith about a tea they believe they are sharing, with one describing it as thin and the other as harsh. Anyone brewing only for themselves never encounters this at all, which is why it comes as a genuine surprise the first time tea is made for guests and why it is so rarely mentioned in brewing advice written for one person.
Why the concentration climbs as the pot empties
Two effects run together and reinforce each other. Extraction continues throughout the pour, so liquid leaving at the end has simply had longer in contact than liquid leaving at the start — and the leaf bed it is passing through on the way out is at its most concentrated by that point, because the water around it has had the longest to load up. Meanwhile the liquid nearest the leaf, which was always the strongest in the vessel, is by geometry the last to leave. Neither effect can be stirred away, and both get worse the slower the pour and the deeper the leaf bed. The result is entirely reliable rather than random: the last cup is always the strong one, in every vessel and with every tea. That predictability is why the convention that the host takes the last cup exists, and why it reads as courtesy rather than as a technical adjustment.
The fairness pitcher, and what it actually solves
The Chinese gongfu answer is to pour the entire contents of the brewing vessel into a second, undivided one — a cha hai, usually translated as fairness pitcher or sharing jug — and to serve from that. Everything is combined and mixed before anything is distributed, so every cup is identical by construction rather than by care. The English name translates the intent rather than describing the object, which is why it sounds odd. The pitcher also does two other useful things that are rarely credited to it: it stops the extraction cleanly by getting all the liquor away from the leaf in one movement, which is exactly what the decanting rule asks for, and it lets the tea settle and cool very slightly before it reaches a cup. It is the single most useful piece of equipment for anyone who brews for more than one person.
Pouring in rounds, which is the older answer
Before the pitcher, and still in several traditions today, the practice is to pour a little into each cup in turn and then come back along the line, two or three times over, until the vessel is empty and every cup has received some of the early liquor and some of the late. Korean darye does this explicitly as part of the etiquette, and so does traditional Chaozhou gongfu with its tight arrangement of small cups. It achieves the same evening-out with no additional equipment at all, and it is worth knowing because it works with any teapot at any table, including a large western one. It is slower than using a pitcher and it requires the cups to be arranged within easy reach of the pot, which is part of why the pitcher displaced it in modern practice and why the cups in those traditions are grouped so closely together.
The same problem in a western pot, with an extra term
A large teapot with the leaf still in it has everything described above plus a fourth effect that is often larger than the other three combined: the tea continues steeping between the first cup and the second, so the second is stronger both because of the pouring gradient and because it was simply brewed for longer. Twenty minutes into a pot the difference is not subtle, and the last cup can be a different drink entirely. This is what the strainer-and-second-pot arrangement of formal English service was actually for, beneath the ritual — one pot to brew, one to hold, and hot water to let down what has become too strong. Decanting a western pot into a second warmed vessel once it has reached time is worth the trouble whenever the pot is not going to be finished quickly, and it is the same move the fairness pitcher makes.
Temperature drifts across the pour as well
The first cup poured is hotter than the last, and if the cups were not warmed beforehand the first also loses more of its heat to cold porcelain than the last does, since the pot has warmed the room and the tray by then. So the difference between cups is not only a matter of strength: it is temperature, and therefore aroma release and perceived sweetness, both of which vary sharply across the range a cup of tea passes through. Warming all the cups before pouring removes one term of this entirely and is the reason the practice exists, quite apart from any ceremonial reading of it — it is the same argument as preheating the pot, applied one step further down. Pouring into a pitcher first removes another term, since everything then leaves the pitcher at a single temperature.