Catholics argue the deuterocanonical books should be included in the canon of Scripture. However that has significant flaws:
1. The Jews didn't consider these books on par with Scripture. The Hebrew canon doesn't include the deuterocanonical books.
Some argue the Jews only canonized the Hebrew Bible at the Council of Yavneh. However, from what I've read, that's hotly disputed by scholars. It's far from established fact.
However, even if it were true, the question parallels questions over the NT as canon. For instance, did the Jews/church decide what should be canonical or did the Jews/church recognize what was already recognized as canonical? For another, why would pious Jews/Christians need an authority (e.g. council) to decide what they could already know from studying the Scriptures and using their own God-given reason?
2. There are fragments and portions of some deuterocanonical books in the Dead Sea scrolls (DSS), but the DSS contain plenty of literature that even Catholics wouldn't consider inspired (e.g. the War scroll, Pesher Habakkuk). So the inclusion of some deuterocanonical books in the DSS doesn't imply anything one way or the other about the deuterocanonical books in general.
Similarly, Codex Sinaiticus contains the deuterocanonical books, but it also contains the Epistle of Barnabas and the Shepherd of Hermas. Catholics don't accept these latter works as canonical.
3. The deuterocanonical books themselves suggest prophecies had ceased in their day. For example, 1 Macc 4:41-46 records:
Then Judas detailed men to fight against those in the citadel until he had cleansed the sanctuary. He chose blameless priests devoted to the law, and they cleansed the sanctuary and removed the defiled stones to an unclean place. They deliberated what to do about the altar of burnt offering, which had been profaned. And they thought it best to tear it down, so that it would not be a lasting shame to them that the Gentiles had defiled it. So they tore down the altar, and stored the stones in a convenient place on the temple hill until a prophet should come to tell what to do with them.
In addition, the Prologue to Sirach suggests its author doesn't even consider Sirach to be Scripture inasmuch as he draws a distinction between the two.
4. If the deuterocanonical books should be part of the biblical canon, which deuterocanonical books? Whose version? The Eastern Orthodox differ from Catholics (e.g. Psalm 151, 1 Esdras, 3 Maccabees, the Prayer of Manasseh). Likewise, what about the deuterocanonical books of the Oriental Orthodox churches? What about the deuterocanonical of the Assyrian churches?
5. If we accept the OT apocrypha, then why not accept the NT apocrypha - at least some of the books? Couldn't one argue some of the apocryphal gospels deserve inclusion in the biblical canon?
6. To my knowledge, Catholics didn't officially include the deuterocanonical books in the biblical canon until the Council of Trent. However, wasn't this decided by a plurality vote with many Catholic bishops on the council either dissenting or abstaining from voting? If the deuterocanonical books are Scripture, then why would so many Catholic bishops fail to see that? And what about Catholic bishops who weren't in attendance?
Also, if it's possible for the deuterocanonical books not to have been officially recognized as part of the biblical canon until Trent, even though the deuterocanonical books had always been part of the canon, then why would Trent be needed in the first place? Just to rubber stamp it? Yet how many Christians throughout church history until Trent even thought all the deuterocanonical books were inspired and on par with Scripture?
7. Perhaps Catholics would respond there is a long history of church fathers who thought so. Church tradition has established it to be the case. Church fathers like Clement of Alexandra, Irenaeus, Tertullian, and Augustine believed the deuterocanonical books were inspired. For one thing, there's nothing necessarily sacrosanct about church fathers and church tradition. Church fathers have made plenty of mistakes. For example, some church fathers quote the Sibylline oracles, but that hardly means the sibyls were inspired by God.
8. At best, the church fathers who held the position that the deuterocanonical books are Scripture held it because they were following the Septuagint (LXX). Of course, this should be offset by the evidence of and from the Hebrew canon.
Moreover, consider Peter Williams' lecture "Why I don't believe in the Septuagint". As Williams points out, there's not a single homogeneous LXX. A first century Jew or Christian wouldn't have necessarily considered the LXX a single unified body of work. Rather, they might've just regarded them as disparate Greek translations of this or that book of the Hebrew Bible.
Perhaps like how we might see there are various English translations of the Bible (e.g. ESV, NIV, CSB, KJV, RSV, Phillips' NT, Lattimore's NT, NASB, NRSV, NLT, CEV, NET, Geneva Bible, Tyndale, Wycliffe, Douay-Rheims, NAB, NJB, JPS), but we wouldn't necessarily categorize all these translations under a single monolithic category called "The English Translation" (TET).