Why is it that only humans commit suicide? Many animals do 'brave' things to protect their children or family, and some male spiders sacrifice themselves so that they can impregnate the females. 

However, humans commit suicide without necessarily any intention to help their kin. Why?
Such behavior does exist in the wider animal world, not just in humans.

See the Wikipedia page on Animal Suicide, particularly the section titled "Suicidal behavior".
(if you have done any preliminary research on this, be aware that your question doesn't reflect it).

There are a number of linked studies in that section, some of which may give you good or relevant information.

What it comes down to is twofold:    


We can't reasonably say that animals are pursuing suicidal behavior for similar reasons that humans do, as we don't have a good enough view into the cognitions of other animals, and
We still don't fully understand the etiology of suicide (much less depression!) in humans, either, which confounds the entire issue.