Hi @Lemonjuice,
This is an interesting topic that you raise. As @utopia mentioned, there was a discussion around the difference (if any) between suicide and euthanasia last year here.
I think the reason people get sad when someone dies is that they miss them. This is what it has been like for me when I have had to have each of my animals euthanized in the past few years. I believe that euthanizing a pet is a sacred part of pet ownership. I hold each of my animals while the vet helps them to make safe passage across the Rainbow Bridge and I have a lot of ceremony around their passing. This is because I experience their passing as an intense loss and I superly duperly miss them. I don't really feel either happy or sad for them as they die. They are animals, they have no concept of death. However, I am glad that I am able to choose the time when they die such that they are not in distress.
I read that you will be needing to euthanize your dog very soon and I'm guessing that perhaps this has brought up some of these things that you are thinking through right now. I'm really sorry that you are having such a tough time at the moment.
You mentioned that you think caring about others is illogical. I disagree. We are biologically hardwired to be a social species. This is because living in groups is more conducive to survival than living alone. We have evolved to have a drive to be with others and to have social bonds because this is most conducive to the survival of the species. That seems quite logical to me.
I found it interesting that you said you know it is selfish for someone to suicide. Many people would disagree with you. I don't think it is selfish - I think that it is an act that is a response to immense pain.
I think perhaps the reason a lot of people feel sad when someone suicides (beyond the grief of missing them as they would due to any cause of death) is because it is often seen as a "waste". That is, I think a lot of people believe that if the person could have held on, things would have improved for them. There are many people who have survived a suicide attempt and gone on to be grateful that they survived. However, there are others (like me) who remain entirely indifferent.
Thank you for raising such an interesting topic.