It's funny. Sometimes you're in a discussion with someone and you wish for an example of something. You want a simple, effective way to help them understand what you're talking about - something you can relate to them with, so you can take it a step further and show them a perspective they otherwise probably wouldn't have noticed.
Sometimes you get an example and really don't fucking want it. Yesterday I was asked how I can deal with death and see life as anything other than pointless. Well, fucker, this is what you get.
This is my cat, Patsy (named for Joanna Lumley's character in Absolutely Fabulous). She's sixteen, and as I write this, she's dying. Her hind legs don't really work; she stopped eating yesterday, she can't drink water properly and she's losing her voice - which might be the most painful part of it for the rest of us. She was given to mimicking the tones of voice we use in greeting each other when one of us entered a room; it looked a lot like she was trying to communicate the way we did. Maybe she was. She's a fucking smart cat. Now she can't do that; she can barely make sounds.
We got Patsy from a shelter when I was thirteen, and she was three. She'd apparently had a bad life before that; beautiful as she was, someone had treated her so badly she almost panicked herself unconscious her first night in the house. Judicious application of cat treats was necessary to get her to come out from under the stereo (oddly, as soon as she came out, she picked up a pen in her mouth and carried it around with her for about half an hour, then never did anything of the kind again).
Now I'm twenty-six. She's sixteen, and fully half my life later she's finally over her fear of the vacuum cleaner...and I'm watching her body shut down over the course of a few days. There are people who'd call this pointless attachment to an animal. I would, quite honestly, be very fucking tempted to hit them in the face. Anyone who's owned and cared for an animal for any length of time can tell you that they very quickly become family, and seem to take on human traits. It's been posited that hanging around humans can affect some animals and raise their intelligence. Regardless of whether it's true, Patsy's the most stark example I've ever seen of why people might think so; she tries to talk to us, copies our intonation. I'm half-sure I heard her try a consonant once or twice. Her intelligence seemed almost comparable to ours, like a toddler who can't quite communicate; she very quickly became a well-loved part of the family. Watching her die is excruciating.
What I'm getting at here is that this is more or less how a materialist and anti-theist* like me reacts to every death of a loved one. The fact that she's a cat doesn't actually change much; the period of grieving is shorter as reality reasserts itself, but the thought of losing her, before the fact, is just as intensely emotive as losing anyone in my family.
What this has in common with a believer's view of losing a beloved pet is that neither I nor they believe that my cat is going to experience an afterlife. She will simply stop. Her clockwork's winding down, and she is going to die and that's it. Soon. Maybe tonight. Her body will become electrically inert, and begin to break down into its component molecules through decomposition. This is, give or take some greater or smaller knowledge of the biological processes involved, how - say - a Muslim or Jew or Christian in my position would also view the coming events. A Hindu or Buddhist, or someone of another faith that involves reincarnation, would have a slightly different view of things; for the three big monotheist groups, though, this works well enough as a comparison.
Where it differs, of course, is that this is exactly the same way I view a human's death. Same processes, with a lot more grieving for various reasons ranging from language and interaction (letting us get a lot more involved with humans than other species) to plain old human conceit making our brains tend to register other humans as more important. I've been told I'm a depressing person because of this; I've been told I shouldn't think such terrible, bleak things. I have had this said to me more than once, by people who really, honestly believed that if I didn't agree with them before my own death I would suffer until the end of time.
Next time someone tells you they'd be depressed without the idea of an afterlife, remember what faith they are; most versions of heaven involve a ringside gloater's seat for watching what happens in hell.
And next time someone mentions to you they think animals go to heaven, thank them from me for at least trying to help.
*Anti-theist, in the late Hitchens' definition: not only do I not believe that religious stories are true, but I think it would be bloody awful if they were.