Actually, she has a point. What are "safe spaces" if not an admission that you can't handle criticism?
An admission that there are certain situations in which you don't want to deal with criticism?
I cannot speak for everyone who has ever used the phrase "safe space", but in my experience when people use it they mean that some places are safe for specific things and others are not. Which sounds like a pretty reasonable idea.
I'm all for engaging with criticism and being open to various points of view, but only when people have the will and mental energy to do so. If someone just wants to vent about something or talk to people they already know are on the same page, they should have a chance for that, too. Hence, safe spaces.
There are infinitely many debates you can have about what places should be safe, whether being safe for X necessarily excludes being safe for Y, etc. But the bare notion of safe spaces doesn't seem that controversial to me.