Negativity can come in so many different forms when you run a small business: clients, competition, the industry...and (the biggest one!) yourself. It's really hard to get through an entire day without it in one form or another. I've struggled a LOT in the past with negativity; both being a negative person (especially towards myself) and treating others negatively.
It was through a lot of maturing (at least I think :) ), years of experiences and lessons from my life coach that I truly learned how to change myself and deal with negativity better. With lots of practice and giving myself grace to be imperfect, over time I gradually changed my view point and attitude, becaming more self aware of my [negative] actions and reactions. Negativity is such a slippery slope, and once you start down that road, it's hard to get off of it.
We are all human. We all make mistakes. Chances are, the negativity that someone is directing at you actually has absolutely nothing to do with you. We tend to displace our anger or negativity to the things we are dealing with in the moment instead of the things that are actually bothering us.
Remember that saying: be kind for everyone you know is fighting a hard battle? It's so true. It's hard to know what's truly going on within every person. Every one is on their own journey and learning lessons specific to them.
One of the biggest lessons my dad taught me growing up is to 'kill them with kindness.' It's his answer to EVERYTHING. It's inevitable in small business (especially when you're starting out and still developing your preferred clientele): getting that one client that no matter what you do, they will never be happy or satisfied. And it sucks. And it's hurtful. Our businesses are our world; our hearts; our blood, sweat, and tears. And right or wrong, we can take things personally.
When it comes to dealing with negative people, being kind is truly all we can do. No matter how badly they treat us or how much their words cut right to our core, I try to hold my head up, smile, listen, and then...just be nice.