As a (presumably) gender-normative person, you can't be expected to "get this issue". But, hopefully, with a bit more knowledge you'll begin to get it and understand why it matters, and can genuinely put people in danger.
There are many parts of the world, including in the United States, where hate crimes against transgendered people are common. This includes cities that we like to think of as progressive and gay friendly. Trans people have been beaten, and even murdered, simply for being trans. So, to be trans in the US, and in many other places, is to live in fear that the wrong person will discover your identity, where you live, etc.
Further, drag personas may very well be the primary social identity of a person. Their friends know them by this name and identity, and may not know of any other. But, when they go to work, go shopping, etc., they may have very different persona that they keep separate from their social identity for their own safety and well-being. People can still lose their jobs for being trans. Trans people can be, and often are, treated very poorly by medical practitioners (particularly poor folks who have fewer options for their medical care). Trans people can be treated very poorly by the legal system in child custody cases. Likewise, trans people arrested for crimes often receive stiffer sentences than non-trans folks, and may experience discrimination and humiliation in the prison system. It is dangerous, on so many levels, to be openly trans.
Transgender is recognized to be a real thing, and not a "disorder", by every major psychological and medical organization in the developed world. But, the popular opinion has not caught up with the science. And, so people who are trans have significant hurdles to leading a happy life free of being bullied, preyed upon, and generally having a lot more challenges than folks who identify as the sex of the body they were born with.
In short, saying, "Setup a business page for that persona or whatever." ignores the reality that trans people live with every day. Revealing that one is trans to the world at large dramatically increases the risk of being trans.
It sucks that our world and society is this way. Someone should be able to dress up fancy on a Saturday night, without fear of being beaten for it, fired from their job, risk losing custody of children, or be denied appropriate medical care. But, we don't live in a world where that's true. Those are the realities of being one of the most hated minorities.
Facebook's policy made it harder for trans people to exist in peace. So, the apology is warranted, and the clarification of the policy is useful. Though, I think it probably doesn't go far enough. And, I think their reasons for being so insistent have as much to do with the value of knowing someone's legal identity, as it does with their assertion that it is the "primary mechanism we have to protect millions of people every day, all around the world, from real harm."