Had some experience with putting a pet to sleep recently. So, of course, it got me thinking about the topic a bit more philosophically. Probably because it helps me to think of the subject in a bit more of a detached way. But for whatever reason, here I go.
First thought, having a belief in something like a pet heaven. I don't think I'll take a stance on the afterlife in this post. What I am concerned about is how the belief in the afterlife will affect whether or not someone goes through with an act of euthanasia.
Belief in the afterlife can help others feel better after having lost someone, whether it's a person or a pet. If you think the deceased are in some kind of heaven, instead of just not existing anymore, it'll probably make you feel a bit of better. Whether or not this afterlife actually exists is not important (for the purpose of making one feel better anyway). What's important is just the belief in this afterlife, since it's the belief itself that makes one feel better.
However, when deciding if one should euthanize someone, whether or not such an afterlife actually exists is important. If one of your main reasons for thinking that someone should be euthanized is that they'll be going to heaven instead of staying in this world and suffering, then the truth of whether or not such an afterlife exists is important. If the afterlife does not actually exist, then one should not factor in the existence of the afterlife when considering euthanasia. If the afterlife does not exist, one should just consider if it's better to go on living while suffering, or not exist at all. These are less comforting options, but it's important to be honest if you really want to make the right and informed decision.
Similar reasoning applies to thinking of euthanasia as killing. Trying to separate euthanasia as something different from killing in one's mind can help make one feel better about euthanasia. But again, if euthanasia really is killing, one ought to think of it like killing before making the decision whether or not to euthanize someone. This is not to say that euthanasia is not a just killing, but most likely, it is a killing nonetheless and it should be considered such before making that big decision.
It's a shame that weighing the truth may make someone feel worse than if they just believed whatever made them feel the best. But perhaps it is better than looking back one day and realizing that you made the wrong decision because you did not look at the problem honestly.
That said, it can be very hard to do, and I don't know if I could (or even really want to) make myself do it if I were really in situations involving euthanasia...