A lot of what I would have said has already been posted, but basically to sum it up, the SBT’s history (and I know people hate accepting this because it’s awful, but denying it is a disservice to this breed) is heavily seeped in blood sports, dog fighting in particular. And it is mostly from this, that Staffs gained this bad reputation. This is not to say that responsible breeders these days are trying to breed away from this, but there are absolutely still dogs being bred for this awful purpose in underground rings and the history can still run in their genetics - many Staffs are not tolerant/reactive of other dogs.
They were never “nanny dogs”, this isn’t to say that some aren’t fantastic with kids, but no dog is a nanny dog, no dog should be left unsupervised with young children. I’ve seen people that genuinely believe this was the breed’s original purpose, to look after children when the parents were away. Historical citations of this phrase being used are difficult to find (and most seem to end up talking about the American pit bull terrier instead, a different breed) - “nanny dog” is a more recent thing and I really wish it would stop being used because it does no service to any dog being expected to be 100% bombproof with children, and there are far too many idiots out there that take the term literally.
Also, to touch on the ‘locking jaw’ thing. Also a myth. However, look up ‘gameness’, this was a prized trait in Staffs (and still is today, their loyalty and courage is often unmatched) but it was used for a crueler reason; to create dogs so determined to fight that they could have broken bones and they’d still wouldn’t give up. They have a very specific bite style that was selectively bred for, whilst most other breeds will often snap and release when they bite, bull terrier breeds will often hold on with incredible tenacity, and shake (like terriers, see how ratters shake their quarry to break their necks, very efficient!). You’ve seen the videos of Staffs hanging from branches and tyres, or relentlessly hanging off their tuggy toys, this is that fantastic drive in action. This is where the ‘lock jaw’ myth came about, because if they are determined, they will not give up. That, coupled with the fact that these are powerful dogs in a small package, is what can make their attacks (as some people have mentioned as anecdotes here) so deadly. Unfortunately, in the case of an attack (and yes, all dogs can turn, of any breed), the owners are often ill-equipped to handle it and most of the time, didn’t even know that their dog was capable of it. And because of this gameness, which is still seen today in some SBTs, it’s generally difficult for the average person to remove the dog until it’s too late.
Anyway I could go on because I’m really passionate about dog breed history and Staffs in general, they’re a great breed that is sadly filled with a lot of misinformation and fear, BUT people need to do their research and accept that this is a breed that often does not get on well with other dogs/smaller animals due to selectively bred genetics and, in the wrong, inexperienced hands, has the potential to do a lot of damage.