I think it's because they don't understand how you feel.
I also believe it's a transient understanding for those who have been there but aren't right now.
The idea of wanting to die makes no sense. Life is so precious and fleeting, why would you want to end it?
This is how I feel when I'm doing well.
When I'm not doing well, dying makes perfect sense. The idea of wanting to live makes no sense.
Why would I want to carry on with this painful existence, life is short so what does it matter if I go early, who'll even notice?
I don't know about anyone else, but these two opposing thoughts never hold the same weight in my head. One makes good logical sense, the other ludicrous.
When I feel like dying, someone trying to tell me that "It'll get better." "Life is short" "Your loved ones care for you" "You need to make the best of it".
All of it sounds stupid. To the point of being insulting. Having been where they are, I can understand that they mean well, but it makes no sense.
On the other side of the coin however. It's opposite. I understand that a person who feels like dying, really feels lost and hopeless. That death is the only thing that can bring them peace. But right now it makes no sense. It probably will again one day, but not right now.
Empathy is as we are all aware, the ability to see the world through another's perspective. As much as people try to do this, some things may be too alien to really comprehend.
Unless someone has been there, I don't think it's something they can even begin to imagine, let alone understand.
So they go with what they know. Survival.
That, and they really will miss you. Not to mention there really are more options. They are just hard to see right now.
And no, I don't think they want a pet robot. If they did they'd just get a real robot, as they don't need to be fed.