I don't understand why my husband is still grieving the loss of the dog?

Losing a pet can be truly like losing a family member, because it affects the same emotions. Maybe your husband really wanted to keep the dog, so he could be mourning both the loss of the animal as well as not having kept him.

Additionally, one week is pretty short. You're going to need to get onboard with this and support him and show your understanding. 

Try to understand the dog may have been a friend who stuck with him when others may not have. There could be memories associated with the dog, as well. Do everything you can to understand how he feels, and appreciate his kind heart. Not all men are kind.

Maybe, one day, you can consider letting him get another dog you and he could keep together, or even a cat.

Our two dogs each had a bed with their name on it on the floor in our bedroom.  They both passed away in the same year after having them for 14 years.  We couldn't bear to move those beds so they stayed there on the floor in our bedroom for another full year.  Then, my wife cut off the embroidered name off each bed and kept them while we disposed of the rest.  Those dogs were like family.

you are very mean to make him give up his pet

Prepare yourself. You`re getting dumped and kicked to the curb soon. And with good reason.

My bet: he's reliving the anger with having to give the dog away.  You can't "comfort" him because you don't respect his feelings on this.  Over time, he'll get over it.  My wife still tears up when she thinks of a dog that died 4 or 5 months ago.  She had been actually crying about him until about a month ago.  Don't be poking him about this.

Because he DID lose a member of his family.

I had a cat for about 12 years before I had to give her to my parents to take care of when I moved away and married a military guy. She was both indoor and out door so, I didn't want to seclude her in a tiny apartment. My mother took care of her for 7 years until we had to put her down. I took it a lot harder than I thought. Sometimes losing a pet is devastating. You never know how you're going to grieve until you've lost them for good. Let the man grieve.

How sad for you.  Nothing anybody here can do help you.  

and you won't ever understand how close he felt to that dog--because you obviously have never felt that way.  and he will never understand how it is nothing to you...so you will just need to accept that he feels that way and let him grieve, respectfully...….....and hopefully he will not reproach you for not having those kinds of feelings.

It WAS a family member. Even if you think it's stupid, the guy clearly loved that dog as much as you might love a human family member. That's not common but it's not unheard of town love a dog that much...

First, you are no dog lover, so how can you understand, the bond behind a man and his dog? He raised it like child, he gave it up for you. People are many times closer to their pet than some crap family member. Maybe you are in need of seeing a therapist. Sorry for your husbands loosing his buddy.