Why are the Shavuot loaves baked with leaven?

Because the Torah explicitly commands it — and the grammar is unambiguous.

"From your dwellings you shall bring two loaves of wave-offering: two-tenths of an ephah of fine flour they shall be; with leaven they shall be baked — firstfruits to the LORD." — Leviticus 23:17

The Hebrew phrase חָמֵץ תֵּאָפֶינָה (chametz te'afenah) is a Niphal imperfect third-person feminine plural: "they shall be baked [with leaven]." It's a positive command, not a permission.

This is striking because Leviticus 2:11 appears to forbid leaven in grain offerings: "Every grain offering that you bring to the LORD shall not be made with leaven." But the very next verse (Lev 2:12) qualifies: "As an offering of firstfruits you shall bring them to the LORD, but they shall not go up on the altar for a pleasing aroma." In other words, leaven and honey could be brought as firstfruits — they just couldn't be burned on the altar. Shavuot's two loaves are exactly that: firstfruits brought to the LORD, waved before Him (the Hebrew is lechem tenufah, "bread of wave-offering"), and then Lev 23:20 tells us they go to the priests as food. They aren't burned. They are eaten.

So the rule and the exception fit together. What Lev 2:11 forbids on the altar, Lev 2:12 and Lev 23:17 permit — indeed require — as a wave-offering. Within the festival calendar of Leviticus 23, Shavuot's loaves are the only leavened offering. The Torah does explicitly require leavened bread in one other ordinance — the thanksgiving peace-offering of Lev 7:13, where loaves of chametz accompany the todah sacrifice. But on the annual festival cycle, only Shavuot leavens its firstfruits bread.

What does the leaven represent? Scripture doesn't spell it out. But it's worth noticing that the New Testament repurposes the bikkurim vocabulary — translated into Greek as ἀπαρχή, aparchē — for a people, not a grain. James writes that believers are "a kind of firstfruits of his creatures" (Jas 1:18). Revelation 14:4 calls the 144,000 "firstfruits to God and to the Lamb." The leavened loaves of Shavuot are presented to the LORD as firstfruits — a dough that has been worked through, fermented, transformed. If Shavuot's offering foreshadows the presentation of a people, then the leaven signals something true of any real people: they have been changed.

Scripture doesn't make that leap in so many words. The Torah gives the command, marks the contrast with altar-burnt offerings, and waits. Centuries later, when the Spirit is poured out at Pentecost (Acts 2) on the day of the wheat firstfruits, a community of three thousand souls is "added" (Acts 2:41). The reader can weigh the connection.

For the full treatment — including the morphological note, the Lev 2:11/2:12 qualifier, and the New Testament firstfruits typology — see the full study: Count Fifty Days.