Err's activites

I got the chance to adopt a pet today!
My family and I went to the shelter earlier, and while they were looking at the other animals, I went to the dog section.
While I was there, I saw a dog that looked exactly like my dead dog. I nearly lost it when I saw the dog. I tried petting it, but it ran into a corner. I was about to leave when my parents saw me and looked at it.
They almost cried, and they hugged me and pointed at the dog and said we should get it.
I wanted to, but I had to ask why.
They told me it's because "She's our (dog's name)!" "She's been reborn to meet you!"
I stayed calm and said that it wasn't, and could never, be her. Replacing what the dog has been through in it's life and replacing it's whole identity with someone that's very dear to me is just unfair.
Doing that just for me to feel happy about my dead dog "coming back to meet me" will never sit right with me.
It's not fair to my dead dog or the shelter dog.
Then a staff came by and apparently overheard it, because she said "Well, sweetie. Your old partner came back to have you again in it's life, even after spending a life with you. Isn't that sweet?"
I felt really disgusted and mad, so I told my parents I'd leave first and just ran home, regardless of them chasing after me or trying to stop me.
It was really sudden, and it happened 3 hours or so ago and I'm still a little mad, so I've just been in my room. I'll apologize later.