I can't see how taking the life of someone who wants to live is any better than preventing someone who wishes to die from ending theirs. Correct me if I'm wrong, but it seems to me that a common theme on this site is wishing that we had more control over our lives. I know this is true for me at least. Almost every facet of our lives is decided for us by something else, be it our genetics, our parents, or any number of various people or natural processes that have power over us. One thing we do have autonomy over is the decision to live or die, and I can't believe it's right to rob someone of that autonomy.
If someone desires to die, I have absolutely no issue with them receiving assistance from others, so long as it's their choice.
Dogs hardly have the same ability as humans to understand what death is or the potential suffering they'll go through in the future if they continue to live. Though perhaps not ideal, I think it's pretty necessary that humans make that decision for them. People, on the other hand, can make that decision for themselves.