Emotions are an important driving force in everyone's life. As such you must accept and react in a smart manner regarding your partner's emotions, or else you may find yourself interacting with someone that resents you. The best way regarding properly responding to your partner's emotions is for you to actually have experienced them for yourself in the past so that you know how it feels to be inside your partner's skin.
On the other hand, if you are on the receiving end of an emotionally dismissive treatment, you must know that there is some chance that your partner is not actually aware of your feelings or the actions that lead to you feeling this way. This is why talking openly about the problem is always the best action to take. On the other hand, if the relationship has gone far away from the normal track, or if your partner just doesn't want to talk, then you should seriously consider pulling the plug and walking away.