When you want to adopt a dog, a lot of people are only wanting purebred pets. Having a purebred pet can make you stand out. They can be registered, they have great looks, good bloodlines, shown in competitions, they are bred for specific needs and tasks, etc. What people don't realize about purebreds is the problems. Yes, your pet may be top of the line with good bloodlines, but how many times has the mother been bred? Over breeding a female can lead to genetic and health problems in the litters. Every purebred has certain faults. Labs have hip problems, teacups have heart problems, dachshunds have back problems, etc.
When you get a mixed breed dog they are cheaper and sometimes prettier. You can get good qualities of two breeds. Sometimes you can reduce the issues that come with purebreds such as aggression issues or other tendencies. You can get the looks of one breed and the heart of another. Sometimes mix breeds can look purebred. When you get a purebred you can eliminate or greatly reduce the faults that come with certain breeds. For example. If you get a dachshund mix as opposed to getting a purebred dachshund you can reduce the chance of the back problems of a purebred. Or if you get a mixed breed lab, the dog it is mixed with may not be prone to hip dysplasia. Sometimes it eliminates the behavioral problems of certain breeds. A good example of this is a chihuahua mix. Chihuahuas are known for being very snippy and shaky dogs. If you mix the breed with a loving breed that is known for being family based such as a corgi or pom, it eliminates the chance of them being aggressive.
When you get a mixed breed you are saving a life because not a lot of people will get mixed breeds and they end up in shelters. There is nothing wrong with getting a purebred, but that doesn't mean that they are better than mixed breeds.