It doesn't sound like you've ever spent any time at the gym. Nothing's going to tear. You just won't be able to do it. Period. That's what failure means.
The near occasion of sin that constitutes hitting a unisex gym or the needless exposure to ɧoɱosɛҳųαƖs in all-male gyms I avoid like the plague. I do, however, have a regular exercise routine that I perform at home so I know what you're referring to. You wouldn't be able to
complete the rep, but you could pull the muscle easily at any point while attempting to do the next one and yes, that has happened to me. Pushups like most exercises you can do without equipment involve multiple muscle groups and body structures, so lots of things can go wrong. Muscle failure can easily occur mid rep and if you're not careful you can easily hurt yourself. For those who are on a regular routine, they can develop inflammation from overdoing it (too many sets or doing it wrong) which could leave them vulnerable to injury the next time... this is common knowledge!
It happens occasionally even to pro bodybuilders, who can skip right over pulling or minor tearing and rip entire tendons or ligaments off the bone. If you're working out under normal circuмstances
and you know proper form
and you know when to listen to your body then it won't be a problem, but when you've got someone terrorizing you to keep going it's more than possible. You're not putting yourself in the shoes of young kids who wouldn't know better, who wouldn't know what proper form is necessarily, and who might make the effort to push past failure because they are more terrified of their father than they are of hurting themselves.