The biggest problem of people underevaluating this sort of illnesses is the general belief of the proper existence of abstract and poetic entities like souls and minds. Most people in fact don''t relate this type of illnesses to brains (which is the true place of the disease) but they think of them as weirdnesses of minds and souls. I think that mental diseases would have given more credit if people thought about them like illnesses of brain. Thinking of them as peculiarities of minds risks to downgrade them to pure strangeness.

Another factor which contributes to the wrong attitude towards this type of illenesses is the fact that they affect personalities. People are scared of thinking of personalities as a result of chimical reactions and so they struggle in giving credit to organic therapies for mental diseases. If they did they would accept the fact that personality is nothing but brain's activity and this is unacceptable for most people across the world.

Hope this can be useful for your question!

Well, there is something called ignorance still exist in this world and those people you are talking about are the victim of their own ignorance. 

Apart from that,  our science has not been progressed much on our mental aspect unlike our physical aspect. So, most of the people think that depression, anxiety or any such overwhelming and uncontrollable emotional outburst can be controlled by self which is not true for all.