(CNN) The Independence Day "road rage incident" in Texas that left two children severely burned didn't have to happen, Harris County police say.

The confrontation between the suspect who caused the children's injuries and their father lasted for about 20 minutes -- long enough for either man to have walked away before harm was done, said Sheriff Ed Gonzalez in a Monday press conference

It all began with an everyday rudeness on the highway, said Gonzalez: "Somebody cut someone off."

Next, the two male drivers "exchanged words" and pulled into a gas station parking lot, according to Violent Crimes Unit Deputy Tom Turner.

Both men got out of their vehicles and a long argument ensued. During their verbal skirmish, Bayron J. Rivera, 18, took out a firearm. At this point, his opponent returned to his car and started to drive away with his wife and two children and the bundle of fireworks he had just purchased.

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