This is a hard question to ask yourself. Depending on who you ask, you may feel shamed and judged just for asking this question.
Please don't. I am here with empathy and honest advice, as I have been in your shoes before.
So...should you give up your dog? There are two main factors I will tackle today.
1. Is Your Safety at Risk?
First and foremost, if you or your family are in danger from an aggressive dog immediate action is necessary.
If a lifestyle change, and some dedicated work are not possible for your family, then yes, please give your dog to a no-kill shelter or rescue (information below). This removes your family from immediate danger, and puts the dog at the best chance to be re-habilitated and placed with another family.
Depending on the severity of the aggression, there are options to send the dog to re-hab and then return the dog to the owner. A lifestyle change and dedication to training will be top priority for the future of the dog.
2. Is the Dog a Good Fit for Your Family?
Believe it or not, some dogs are prone to anxiety, stress, tension, and even fear-induced aggression in the wrong situations.
For example: a dog prone to anxiety and stress may not be a good fit for an owner with a stressful job. Or a dog that has fear-induced aggression to be in a home that has a very lively social scene.
If the dog and your lifestyle do not fit, please do all in your power to re-home your dog to a family that complements the dog's temperament. There are also no-kill shelters and rescues as well. (Information below)
There are many reasons why the question "should I give up my dog?" will cross your mind. I am not here to tell you what's best for your family, or pass judgment. But please, somewhere in your considerations, consider the future of your furry friend.
Ask yourself "what actions can I take that will give the dog the best possible future considering the circumstances?."
Most of the time, a little training is all that it takes.
Rescues and No-Kill Shelter:
Rescues: Rescue Rovers, CAWS
No kill shelter: South Utah Valley Animal Shelter