You should be proud of your ability of regulate your emotions such that you can make the decisions based on logic and reason. But also take the time to process your emotions. It would be illogical to deny them. Even Vulcans need time and effort to do that!

And these emotions exist for a reason. I’m certain this dog must have had a wonderful last leg of it’s life, since they had someone that cared for them so much, that it hurts you to finally have to make the decision to put the dog down.

Live long and prosper, so that many more may experience your love.