The early scholars, known as the ‘Church Fathers’, agree that the book of Matthew was first written in Hebrew:
Papias (ca. 130 after Yeshua): “Matthew composed his work in the Hebrew dialect, and each translated as best they could.”
Irenaeus (ca.170 after Yeshua): “Matthew also issued a written Gospel among the Hebrews in their own dialect.”
Origen (ca. 200 after Yeshua): “The first [Gospel] is written according to Matthew, the same that was once a tax collector, but afterwards an emissary of Yeshua the Messiah, who having published it for his believers, wrote it in Hebrew.”

The words that Yeshua said in Hebrew were perfectly understood by his listeners. But once they were written they became unclear and vague because the vowels were not recorded along with the consonants in the Even Bojan Hebrew Matthew.

The Greek manuscripts render Matthew 10:34 as

Matthew 10:34 [The Scriptures - TS]
“Do not think that I have come to bring peace on earth. I did not come to bring peace but a sword,
(Words of Yeshua in purple)

The same saying is registered in Luke 12:51 but instead of the word ‘sword’, the term division is used 

Luke 12:51 [TS]
Do you think that I came to give peace on earth? I say to you, no, but rather 'division'. 

Why this difference?
One tradition registers ‘sword’: Matthew 10:34μάχαιρα (sword)
another one registers ‘division’: Luke 12:51διαμερισμός (division)

The context in both traditions speaks of the confrontations and divisions that may come as a result of identifying with Yeshua of Nazareth or following him.
Notice the verses that follow

Luke 12:52-53 [Hebraic Roots Bible - HRB]
52 For from now on five in one house will have been divided, three against two, and two against three.
53 Father will be divided against son, and son against father; mother against daughter, and daughter against mother; mother-in-law against her bride, "and the bride against her mother-in-law."

It could be that the difference in rendering is because this teaching may have been given on more than one occasion with different terms and each tradition recorded it as they remembered it.
But the word ‘sword’ seems to be a symbol of war and slaughter.

The Hebrew text of Matthew recorded in the treaty called Even Bojan says the following

Hebrew Matthew or Even Bojan 10:34
אל  תחשבו  שבאתי  לשום  שלום  בארע  אלא  חרב  
Do not think that I am establishing peace on earth, rather חרב 

As it is written in the Even Bojan without vowel points the word חרב can mean:
חֶרֶב (sword)
חָרַב (struggle, fight, confrontation); in 2 Kings 3:23 we see this term as well

2 Kings 3:23 [HRB]
...The kings fighting have fought one another...

Therefore, reading the text of Matthew with this vocalisation, similar to the rendering in Luke 12:52-53 which uses the word ‘division’ instead of ‘sword’. Division or confrontation ismore in harmony with the context of Matthew 10. So we could read Matthew 10:34-36 as follows

Hebrew Matthew or Even Bojan 10:34-36
Do not think that I am establishing peace on earth, rather confrontation
I am separating the people: the son from his father, and the daughter from the mother.
The opponents will be the ones we love.

What Yeshua said in Hebrew was well understood. But once his words were written, some became vague because the vocals were not written with the consonants.
Source: Avdiel Ben Oved; translated by Nazarene Notes.