To understand scriptures safely, it is important to use good tools. For most laypeople, a good Catholic bible commentary is indispensable. Some of the best ones available including the one volume New Jerome Biblical Commentary, or the New American Study Bible, or the Ignatius Study Bible, or the Navarre Bible series.
Another good tool is a solid bible study program or series. Among many good ones out there, perhaps the most widely used today is the Little Rock bible study series.
As to the passage you mentioned, you probably meant Luke 12:51-53, which says:
51: Do you think that I have come to give peace on earth? No, I tell you, but rather division;
52: for henceforth in one house there will be five divided, three against two and two against three;
53: they will be divided, father against son and son against father, mother against daughter and daughter against her mother, mother-in-law against her daughter-in-law and daughter-in-law against her mother-in-law.”
First of all, we must realize that Jesus elsewhere mentioned that the Son of Man came not to judge, but to save (Jn 12:47) and the Son of Man came not to be served but to serve, and give his life as a ransom for all (Mt 20:28).
This shows that Jesus did not want to cause division because division is good. He caused division because division was already there.
The passage just before talks about how He desired fire would come down and burn in us. This is the Holy Spirit, the Spirit of Truth. When the Truth comes into our life, the ambiguous things in us would be clarified. But people who cling to sin do not like clarity, because clarity would expose them as sinners. Clarity, or Truth, forces us to choose right or wrong, to change or to harden. I either acknowledge the Truth and my wrong, and so choose to repent and change, or I will have to harden my erroneous position, and oppose those who try to tell me otherwise.
This was what happened to Jesus. People around Him experienced the Truth, the fire of the Holy Spirit, and they had to make a choice. Those who were humble — the sinners and the poor — repented and embraced the gospel. The proud and the arrogant — the Pharisees, scribes, Herod, Pilate — felt threatened and so hardened their hearts, and murdered Him.
But this is not the end of the effect of Truth. Division is necessary to expose our errors. It is like good medicine for a chronic illness, it needs to first bring out the pus and rot, which is painful, before it gets better. Errors need to be exposed to all to show how illogical and evil it is, so that it can be renounced and redressed. Division itself is evil; but God sometimes allows it to expose sins so to bring forth healing and renewal.