The analogy in the OP is about helping somebody live.
Providing people with information about suicide is about helping somebody die.
I think that's a pretty significant distinction.
Since this is about helping another person die, what if instead of being on an internet forum, you put yourself in a room with them. They want to die, but they don't have the means,. You have a lethal dose of drugs in your possession. Do you give them the drug, or do you withhold it from them? Do either of these options imply an ego problem or any other problem?
If you withhold the drugs, I am definitely not going to judge you for that.
Now, if you refuse to give up information about support animals, then yeah, I'm going to judge you all day long.