My AH tried to delay putting our beloved cat down when she was so, so sick after a long 17 years with us. It had nothing to do with anything except that he was too emotionally immature to handle the responsibility & reality of it. He was so blinded by his own issues that he never saw all of her suffering. He just knew he loved her & wanted to keep her around much the way a child sees issues like this. That doesn't make it ok - we had it out & I told him to say his goodbyes. It wasn't any easier for me to let go but it WAS harder for me to watch her suffer since I wasn't numbing the pain with alcohol.
I pray your furry friend passes on peacefully & quickly.