When someone says something you don't like, that challenges your perception of how life is, or challenges how you see yourself, it is your choice how you respond to that. You have a choice as to whether you take it personally.
If you react in a negative, unconstructive way, take some time out to reflect on what happened leading up to that moment. How were you feeling at the time when they said it? That is to say, what particular "state" were you in? Did you focus on what you heard (did you turn up the volume?) or what you saw? Did you blow things out of proportion (make a mountain out of a molehill)? Did they give you a particular look that really pushed your ego button?
The key is to learn from each situation and grow. You can then be prepared should a similar situation occur in the future. You should not expect difficulties to present themselves but you should be as prepared as you can be to meet them. Prepare for everything, yet expect nothing.
Keep an open mind and new solutions will present themselves to you. You can choose to respond a different way. Be aware of your own internal tension and take deep breaths to release it. Tap into source (see previous post on Short meditation for connecting to Spirit) and respond from a centred space. Socrates, the great ancient Philosopher, took time to go into a meditative state before meetings.
Try asking questions to find out why the other person said certain things or acted a certain way. If you allow them to respond in their own time, in their own way, then "in-sight" will come your way. Insight is literally to see inside, to understand the deeper reasons.
You might try asking open-ended questions such as "why do you believe...?" or "what makes you say...?" or "where did you learn that...?"
It is important to ask with the intention of discovering more about the other person, so that you can better understand them. Quite often the reason we fall into arguments is because we have one way of looking at the world and the other person has their own unique way. Therefore, you need to learn to be fluid and shift your frequency so that you can see with their eyes.
Note that if your intention is to manipulate the other into your way of thinking or behaving, however, then the outcome of the conversation is likely to be a negative one. If your intention is pure and you seek to enter a neutral space whilst putting aside your agenda, you allow yourself the possibility of transcending your own limitations.
If the other person is limiting the way they interpret life, your intention and neutral space will allow them to question their internal beliefs and perceptions. The likely result will be that they will see and understand your side of the coin, if only because you have endeavoured to see and understand theirs. The law of reciprocity then takes effect and produces a helpful, angst-free outcome for both parties.
Make your conversations fun. You don't have to agree to get on, so detach from your need to be right!