Wikipeadia says of this book, “The Book of Tobit (Book of Tobias in the Vulgate; from the Greek: ?????, and Hebrew: ???? Tobi “my good”, also called the Book of Tobias from the Hebrew ????? Tobiah “Yahweh is my good”) is a book of scripture that is part of the Catholic and Orthodox biblical canon, pronounced canonical by the Council of Carthage of 397 and confirmed for Roman Catholics by the Council of Trent (1546). It is listed as a book of the “Apocrypha” in Article VI of the Thirty-Nine Articles of the Church of England (Article VI at episcopalian.org). Tobit is regarded by Protestants as apocryphal because it has never been included within the Tanakh and considered canonical by ancient Judaism.”

TurretinFan writes:

The book of Tobit is told from a first person perspective by a man called “Tobit.” The book begins: “The book of the words of Tobit, son of Tobiel, the son of Ananiel, the son of Aduel, the son of Gabael, of the seed of Asael, of the tribe of Nephthali …” (Tobit 1:1). One reason to reject the canonicity of the book of Tobit is that Tobit seems to have a very foreshortened view of Israel’s history, even when it comes to his own autobiography.

“Tobit” continues the self-description above with this: “Who in the time of Enemessar king of the Assyrians was led captive out of Thisbe, which is at the right hand of that city, which is called properly Nephthali in Galilee above Aser.” (Tobit 1:2)

The very first issue is trying to identify this supposed king of the Assyrians. The Assyrians don’t have one by exactly this name, but the best guess we have about who the author of Tobit was trying to identify is this event:

2 Kings 17:1-12
1 In the twelfth year of Ahaz king of Judah began Hoshea the son of Elah to reign in Samaria over Israel nine years. 2 And he did that which was evil in the sight of the Lord, but not as the kings of Israel that were before him. 3 Against him came up Shalmaneser king of Assyria; and Hoshea became his servant, and gave him presents. 4 And the king of Assyria found conspiracy in Hoshea: for he had sent messengers to So king of Egypt, and brought no present to the king of Assyria, as he had done year by year: therefore the king of Assyria shut him up, and bound him in prison.

5 Then the king of Assyria came up throughout all the land, and went up to Samaria, and besieged it three years. 6 In the ninth year of Hoshea the king of Assyria took Samaria, and carried Israel away into Assyria, and placed them in Halah and in Habor by the river of Gozan, and in the cities of the Medes.

7 For so it was, that the children of Israel had sinned against the Lord their God, which had brought them up out of the land of Egypt, from under the hand of Pharaoh king of Egypt, and had feared other gods, 8 And walked in the statutes of the heathen, whom the Lord cast out from before the children of Israel, and of the kings of Israel, which they had made. 9 And the children of Israel did secretly those things that were not right against the Lord their God, and they built them high places in all their cities, from the tower of the watchmen to the fenced city. 10 And they set them up images and groves in every high hill, and under every green tree: 11 And there they burnt incense in all the high places, as did the heathen whom the Lord carried away before them; and wrought wicked things to provoke the Lord to anger: 12 For they served idols, whereof the Lord had said unto them, Ye shall not do this thing.
The twelfth year of Ahaz corresponds to about 728 B.C.

On the other hand, the Scriptures tell us that people of Naphtali were carried off by Tiglathpileser:

2 Kings 15:29
In the days of Pekah king of Israel came Tiglathpileser king of Assyria, and took Ijon, and Abelbethmaachah, and Janoah, and Kedesh, and Hazor, and Gilead, and Galilee, all the land of Naphtali, and carried them captive to Assyria.
(approximately 758–737 BC)

Notice that the captivity mentioned there includes Galilee, which is the region that Tobit claims to have haled from.

Even if we somehow blend out these seeming inconsistencies, we are left with a man who was around in the 8th century B.C.

Moreover, Tobit claims that it was in his youth that Naphtali fell out with all the tribes from worshiping God in Jerusalem.

Tobit 1:4-5
4 And when I was in mine own country, in the land of Israel being but young, all the tribe of Nephthali my father fell from the house of Jerusalem, which was chosen out of all the tribes of Israel, that all the tribes should sacrifice there, where the temple of the habitation of the most High was consecrated and built for all ages. 5 Now all the tribes which together revolted, and the house of my father Nephthali, sacrificed unto the heifer Baal.
There are a couple of problems with this. Primarily, the problem is that this is an event that took place in the time of Rehoboam, son of Solomon. That date is roughly 961 B.C. Secondarily, the problem is that although the people of Naphtali sacrificed to the calf and to Baal, those are really two different things (as can be seen in 2 Kings 17, above).

As you can see, this would imply that Tobit was about 200 years old.

But Tobit tells us his total age.

Tobit 14:1-11
1 So Tobit made an end of praising God. 2 And he was eight and fifty years old when he lost his sight, which was restored to him after eight years: and he gave alms, and he increased in the fear of the Lord God, and praised him. 3 And when he was very aged he called his son, and the sons of his son, and said to him, My son, take thy children; for, behold, I am aged, and am ready to depart out of this life. 4 Go into Media my son, for I surely believe those things which Jonas the prophet spake of Nineve, that it shall be overthrown; and that for a time peace shall rather be in Media; and that our brethren shall lie scattered in the earth from that good land: and Jerusalem shall be desolate, and the house of God in it shall be burned, and shall be desolate for a time; 5 And that again God will have mercy on them, and bring them again into the land, where they shall build a temple, but not like to the first, until the time of that age be fulfilled; and afterward they shall return from all places of their captivity, and build up Jerusalem gloriously, and the house of God shall be built in it for ever with a glorious building, as the prophets have spoken thereof. 6 And all nations shall turn, and fear the Lord God truly, and shall bury their idols. 7 So shall all nations praise the Lord, and his people shall confess God, and the Lord shall exalt his people; and all those which love the Lord God in truth and justice shall rejoice, shewing mercy to our brethren. 8 And now, my son, depart out of Nineve, because that those things which the prophet Jonas spake shall surely come to pass. 9 But keep thou the law and the commandments, and shew thyself merciful and just, that it may go well with thee. 10 And bury me decently, and thy mother with me; but tarry no longer at Nineve. Remember, my son, how Aman handled Achiacharus that brought him up, how out of light he brought him into darkness, and how he rewarded him again: yet Achiacharus was saved, but the other had his reward: for he went down into darkness. Manasses gave alms, and escaped the snares of death which they had set for him: but Aman fell into the snare, and perished. 11 Wherefore now, my son, consider what alms doeth, and how righteousness doth deliver. When he had said these things, he gave up the ghost in the bed, being an hundred and eight and fifty years old; and he buried him honourably.
So, Tobit was 158 when he died. Moreover, Tobit was only 85 when he went blind. But Tobit went blind after the captivity. Tobit 2 explains, Tobit 2:1-10:
1 Now when I was come home again, and my wife Anna was restored unto me, with my son Tobias, in the feast of Pentecost, which is the holy feast of the seven weeks, there was a good dinner prepared me, in the which I sat down to eat. 2 And when I saw abundance of meat, I said to my son, Go and bring what poor man soever thou shalt find out of our brethren, who is mindful of the Lord; and, lo, I tarry for thee. 3 But he came again, and said, Father, one of our nation is strangled, and is cast out in the marketplace. 4 Then before I had tasted of any meat, I started up, and took him up into a room until the going down of the sun. 5 Then I returned, and washed myself, and ate my meat in heaviness, 6 Remembering that prophecy of Amos, as he said, Your feasts shall be turned into mourning, and all your mirth into lamentation. 7 Therefore I wept: and after the going down of the sun I went and made a grave, and buried him. 8 But my neighbours mocked me, and said, This man is not yet afraid to be put to death for this matter: who fled away; and yet, lo, he burieth the dead again. 9 The same night also I returned from the burial, and slept by the wall of my courtyard, being polluted and my face was uncovered: 10 And I knew not that there were sparrows in the wall, and mine eyes being open, the sparrows muted warm dung into mine eyes, and a whiteness came in mine eyes: and I went to the physicians, but they helped me not: moreover Achiacharus did nourish me, until I went into Elymais.
Note as well that he refers in this passage to remembering the prophecy of Amos, but Amos prophesied during the reigns of Uzziah of Judah and Jeroboam II of Israel:

Amos 1:1 1 The words of Amos, who was among the herdmen of Tekoa, which he saw concerning Israel in the days of Uzziah king of Judah, and in the days of Jeroboam the son of Joash king of Israel, two years before the earthquake.

This is in a window from about 808-770 B.C. So, this window begins more than 100 years after division of the kingdoms, making it impossible for a man who was 85 to have been around at the time of the division of the kingdoms.

There are more issues with Tobit’s history than this (for example, Senacharib seems to be inaccurately described), but this is one glaring issue.