Disagree. What if the person is depressed enough that they can no longer bring themselves to care about being called a coward.
It's pretty common for suicidal people to care about how their suicide impacts those around them. In terms of that suicide can be an act of anger; it's something people tend to contemplate particularly when they lack hope, so it could perhaps be called and act or desperation or of uncreativity (inability to think of other viable solutions). I'd also say it can be a selfish act because it prioritizes one's own pain over the effetc one's death will have on others.
I don't think cowardice is even relevant and I think Pyraxis is right; that 'suicide is cowardly' is something that gets told to people who are openly contemplating it on the (probably misguided) hope that this will dissuade them. Worse, it kind of invalidates the genuine distress they're in- it's certainly not cowardly to suffer and to want to not suffer; it's just human. It also goes back to the issue of anger.
Having said all that, to
Kevv, and in general: There pretty much always less extreme solutions than suicide (THAT cliche is true), but if you're depressed enough that you're contemplating it, you're probably not thinking at your full problem-solving capacity; that's why it can be really useful to talk to a counselor.