The Torah specifies in (Exodus 12:19) that the laws of Passover apply to both "the proselyte and the citizen of the land." The Mekhilta explains why this explicit mention of the convert was necessary — and the answer reveals something fundamental about how the Torah constructs its legal categories.
The Exodus was an event that happened to Israel and Israel alone. The Israelites were the ones enslaved in Egypt. They were the ones who experienced the ten plagues, the death of the firstborn, the splitting of the sea. The entire framework of Passover commemoration — the matzah, the bitter herbs, the prohibition of chametz — is rooted in what happened to a specific people at a specific moment in history.
A proselyte, by definition, was not there. Their ancestors were not slaves in Egypt. They have no personal or familial connection to the events being commemorated. Without an explicit verse including them, one might logically conclude that Passover laws simply do not apply to converts. The commemoration belongs to those whose forebears actually lived through it.
The Torah preempts this reasoning by naming the proselyte directly: "whether he be a proselyte or a citizen of the land." The convert is bound by the same obligations as the native-born Israelite. Their adoption of the covenant is complete and retroactive — as if they, too, had left Egypt.
The Mekhilta then extends this principle: the same applies to all commandments rooted in events that transpired only with Israel. Wherever the historical basis might seem to exclude converts, the Torah's explicit inclusion overrides that logic.