If dogs could talk, would society think twice before euthanizing?

I think it would make a huge difference because then would not just have feelings but a superior intelect so therefore it would be much easier to identify the problem and solve more humanly rather then have one solution for all problems.

You are lumping a lot of different things together here - "cancer, sickness, deafness, blindness, homelessness, handicapped mobility, and aggresiveness" - so, there is no single answer to your question. But, just as some people request that their suffering be ended - some animals would also request that their suffering not be prolonged and that they be quietly and peacefully euthanized. And, if you really want to see euthanization stopped; the place to start is with spaying and neutering.

It is nice that you brought this up. I think that people will really have second thoughts on doing this things if dogs can really be understood. There is just something with this dogs that even without them saying a word, you would feel so bad even in just hurting them, more in taking their lives. I think that taking a life in general should not be done in any way. I am sure that even the smallest living thing will be afraid from anyone who would wish to end their lives. I think that we will live fine having no one willing to take a life.