I don't think anyone agrees with all of that, but I do think the following applies:
You can't get a pedigree - I've never really seen this. But I do think it's important to be aware about where your dog is coming from - their health, their breeding, the breeds general temperament and what health checks are necessary.
You can't work - I don't think working full-time and owning a dog is compatible unless you can afford daycare or regular visits from a dog walker, or of course you work from home/can take the dog with you. Dogs deserve more than being left home alone for 8+ hours a day while you're at the office.
You can't have any other animals - of course this isn't true, but it's important to recognise the needs of your existing animals first. A terrified house cat plus a dog isn't going to a great combination, after all.
You can't adopt - some people are wary about rescues, especially in cases where you know nothing about the animals history or temperament (for example when people import dogs from abroad).
You can't get a puppy - Of course people will advise rescue because there are lots of young dogs/pups in rescue centres, but that doesn't mean you can never get a puppy.
You can't have a child - small children and young dogs/puppies aren't always the best combination. Both require you to have eyes in the back of your head, both are fast and can be clumsy and unpredictable. Sometimes it's better to save yourself the stress!
You can't live anywhere other than countryside with acres of land - definitely never heard this, just people acknowledging that certain breeds won't cope with stairs, and that living on the 3rd floor in a flat will make toilet training much harder than it has to be!