People often talk about emotional intelligence but don't actually say how to get it. Is low emotional intelligence associated with depression? How do we stop the stigma?

I don't think it is related. Depression is depression, has nothing to do with emotional intelligence because that term relates to how you manage stres levels and interpersonal relationships. Depression is a feeling of its own that represent constant sadness and numbness, so it is a feeling on its own, unrelated to anything interpersonal. Emotional intelligence is by my opinion in corelation with people skills and stres management, not a mental illness. Mental ilnesses are a complete different things. Emotional intelligence is connected to a healthy individual with self awareness, that is lacking when you are sick. So that is that.

I believe to be emotionally intelligent you must be empathetic. Learning empathy will help you understand other people's emotions, being able to put yourself in their shoes is key to emotional intelligence, which in turn leads to better communication and relationships. You need not necessarily have the right words to say in certain situations, but your actions/ reactions will be in the right direction. When you understand what a person is feeling or going through, then you should be able to figure out the appropriate reaction/ action. Having said that, even the most empathetic people can still react in a negative way in any given situations, because empathy requires control and discipline, and we as humans are not 100% controlled and disciplined emotionally, otherwise we will be robots! Honestly, do we want someone to be emotionally in control all the time? No, its not human! In regards to low emotional intelligence, i believe it is those people who are too self absorbed and overly consumed by their own problems and emotions that they are oblivious to all those around them, on the flip side of it, some will totally ignore their own feelings and be about the other person regardless of how they are affected by any given matter. There should be a healthy balance and that is emotional intelligence. I believe depression is a standalone condition, a depressed person may be will aware of how they are affecting others, may be will aware of other people's emotions, but the trigger for their depression is overpowering, and therefore they choose to be inconsiderate of others.