The first opinion that one might think of is that you shouldn't be allowed to cause someone to prematurely die because of something we call the "slippery slope," where one thing will lead to the next. If you allow euthanasia in one specific case of a specific disease, you might come to use it in other times when is isn't as necessary.
Here are some examples of people who allowed for euthanasia:
Philosophers- Someone who is disabled is a burden on society and should be eliminated.
Nazi Party- Out of mercy for people who were a burden on society, they were killed.
Holland- They have rules for when euthanasia is allowed and it includes having two doctors give consent but it says nothing about the wishes of the family members.
In Samuel 2 1:5-16, it tells a story of how an Amalekite boy came to David to report that he had killed Saul which caused David to kill the boy. One might think that we could learn that euthanasia is allowed since David killed the Amalekite for killing Saul. However, the truth is that the boy deserved to die because he killed a king.
Next we learned about one of the ten martyrs who were killed in brutal ways. R. Hanina b. Teradion had a wet tuft of wool put on his heart and then he was wrapped in a torah scroll so he would die a slower death when they lit him on fire. The tuft of wool was preventing his death however it was permitted that they take it off to allow him to die less painfully.
From this we learn that we are allowed to refrain from extending a life. Active euthanasia is not allowed, however, something preventing the death is allowed to be removed.
The final law is that if a person is hooked up to a heart- lung machine and it is known that they will never recover it is allowed to be removed in such a way that it is not actively turning it off. One way to do this is to put it on a timer so that it goes on and off and when it goes off, it just doesn't go on again, and another way is that when it is taken out to be cleaned, it isn't put back in again.
I know that this lesson isn't on the happiest of topics but it is an issue that people deal with and an issue that rabbis have debated over for a long time. Moving on to a happier topic, I am proud to announce that I had an amazing morning due to the pancakes with chocolate chips inside that were made at breakfast. Shalom V'lehitraot!