First, it is true that the Jewish canon at the time around Christ excluded the Book of Sirach. The reason for the exclusion was simple. It was written during the time when the prophetic Word of God was silent; there was no valid prophetic line. This "silent period" lasted from Malachi and Artaxerxes’ time to John the Baptist.
Josephus confirms this; "4. From the time of Artaxerxes to our own day all the events have been recorded, but the accounts are not worthy of the same confidence that we repose in those which preceded them, because there has not been during this time an exact succession of prophets."
Melito confirms this; "prompted by your regard for the word of God, expressed a wish to have some extracts made from the Law and the Prophets concerning the Saviour, and concerning our faith in general, and have desired, moreover, to obtain an accurate account of the Ancient Books, as regards their number and their arrangement, I have striven to the best of my ability to perform this task:."
1 Macc. 9:27, 14:41 confirms this; to wit, no prophet at the time of its writing.
Second, to the question whether there is a theological problem with Sirach that prevents its inclusion as inspired (God-breathed) as thus part of Holy Scripture, the answer is yes.
Here are a couple of examples to show that Sirach contradicts Scripture. Translations are from http://www.ccel.org/bible/kjv-apoc/Sirach/.
Sirach 25:24 Of the woman came the beginning of sin, and through her we all die.
Scripture: Man is the origin of sin (Num. 5:6, Num. 16:22, 1 Sam. 2:25). And of course the famous Pauline quote “Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:” (Romans 5:12).
Sirach 33:1 “THOSE WHO FEAR the Lord shall live for their trust is in one who can keep them safe.”
Scripture: Fearing the LORD helps, but that’s not all it takes to live. (Deut. 6:2, 13, 10:12, Jos. 24:14). Indeed, it would take Christ fulfilling the Mosaic Law to live and believing it (Rom. 6:8, Psalm 110:4).
Sirach 41:4 And why art thou against the pleasure of the most High? there is no inquisition in the grave, whether thou have lived ten, or an hundred, or a thousand years.
Scripture: After death comes judgment. There is an inquisition. (Ex. 3:6, Mt. 22:32, Acts 10:42).
To conclude, the Hebrews, Christ, and early Christians knew Sirach was uninspired, contradictory, misleading, and thus is excluded from Scripture.