Question

A. In explaining the contradiction between “For seven days you shall eat matzot” and “For six days,” the Talmud derives, based on the rule: anything that was included in a general rule and then left it… left in order to teach about the entire rule. (And only “in the evening you shall eat matzot” teaches the commandment of matzah on the Seder night.)
What is this strange mechanism of writing a general rule, then partially contradicting it, and from that I understand that the whole thing is limited?
Just don’t write it as a general rule and there won’t be any problems.
I thought maybe the point is that the Torah wanted to say that only matzot may be eaten, and not leavened food. That would explain the nature of the prohibition of leavened food, and that matzah is permitted. And so that we should not understand that there is a commandment to eat matzah every day, it then limited it as above. So it left the general rule in order to teach.
Is that correct? But it is still difficult: to teach the law in such a “crooked” way—why not say explicitly that there is no commandment during all seven days?
B. This derivation seems different from other uses of this interpretive rule, for example:
It says: “And the person who eats flesh from the sacrifice of peace-offerings that is the Lord’s, while his impurity is upon him, that person shall be cut off from his people” (Leviticus 7:20). But peace-offerings were already included among all sacred offerings, and excision had already been stated regarding all of them for someone who eats them in a state of bodily impurity. So when they left the general rule to teach, they did not leave in order to teach about themselves, but rather in order to teach about the entire rule, to tell you: just as peace-offerings are special in that they are sacred items whose sanctity is altar-sanctity, so too everything whose sanctity is altar-sanctity; this excludes items consecrated for Temple maintenance.
And similarly in “kindling left in order to divide the categories”: as it says, “You shall not kindle fire in any of your dwellings on the Sabbath day” (Exodus 35:3). But kindling was included in “You shall not do any labor” (ibid. 20:10). So why did it leave? To compare the others to it, and tell you: just as kindling is a primary category of labor and one is liable for it independently, so too for every primary category of labor one is liable independently. And Rashi on Shabbat 70 wrote that this is the rule of anything that was included in a general rule, etc.
In these derivations, it looks like a completely different type of derivation, a version of an a fortiori model from a paradigm case, where one derives a law for the whole group of laws from one specific law. It is like a narrowed form of building a general principle from a paradigm case, applied to the group of laws that it teaches about.
And not like matzah, where the thing that left the general rule *cancels* the original law.
And regarding these latter derivations, the difficulty I asked about does not apply either; there is no strange wording here of stating a law and then canceling it.
So what exactly is the meaning of this interpretive rule?