Negativity is always around us. It's a key part of life, and there is no avoiding it. People who try to be always positive usually turn out miserable and unfufilled.
Yet, negativity doesn't deserve to be always present. It simply doesn't. A life full of negativity is also a miserable life.
Negative emotions jump from people. When one of us gets upset for whatever reason, and then passess that negativity to another person, through rude, arrogant, hurtful behavior, the chain goes on. I can remember myself many, many situations when I received negativity from one person, and then passed it onto another.
To stop this chain, one needs to dissolve negativity within themselves. It's not easy, of course - someone, who's psyche is fragile, will not be able to handle this. Only someone with a reasonably clear mind can truly get rid of incoming negativity.
So, how do you do this? Well, instead of shouting back at the person that just "sent" you some negativity, just stop, apologize for any misunderstaing, and let them calm down. Then, go for a walk, do something creative, do something joyful, something that makes you feel fulfilled, whatever that is. As with a touch of a magic wand, you'll see how slowly the negative feelings will become weaker and weaker, ultimately disappearing. And the world will be a better place, because you managed to destroy a tiny bit of bad.
Be a hero. Stop the chain.