So in a situation where there is a question of either being kind or being right, choose kindness. There is no need to change the mind of another because you will likely not be successful anyhow, if ever. And what gain is there of any practical importance. Yet another example is when people argue over “quality” comparisons like who is the better singer, or which baseball team will win the World Series. There can be no winner in such an argument.
Even if you succeed in subduing your “opponent”, notice later the guilty feelings you may have as you “showed them off”. Especially if you escalated the argument and supposedly “won” the argument, the other person will feel bad and their ego bruised for nothing except for your own ego growing (which in itself is also a bad thing). The next time you get into such a useless confrontation, notice your mind. Watch the stillness and calmness of the waters start to be pushed up and down (imagine always your mind as a lake, the surface of which will show the degree of calmness). Seek to be still.
In the case of the cars in the intersection, if you simply wave the other car ahead, then the waters of your mind-lake will have been undisturbed, and you continue your day merrily. But then suppose you honk and shout and curse and or gesture at the other driver, then notice your “mind-lake”. Look at it! The surface is not flat and still but there are now waves like during a storm. Don’t ruin your moment and day. If you get angry, your present moments will be ruined for an unspecified and unknown period of time as you have to wait for your “mind-lake” to settle down.