My wife had an interesting point about this fascination with the PGA:
She thinks that what probably happened is that she dominated junior golf at a time when, from a physical perspective, there wasn't much of a difference between boys and girls. Remembering that she's only 16, that girls hit their growth spurts 2-3 years earlier than boys, and that boys gain most of their advantage in strength and explosiveness after they reach puberty, she is very likely accustomed to being the best golfer in her age group - boys or girls.
I have a recollection of just how dramatic that change can be. When I was a junior ski racer, I got my growth spurt a bit later than a lot of my buddies racing in my age group. I have a very distinct memory of finding that some of my buddies all of a sudden got good - VERY good - in a hurry when they hit puberty. I also remember when it finally hit for me, I got a lot bigger, a lot stronger, and a lot better - in a big hurry. I also recall that in the earlier years there was not much difference in results between the best boys and best girls, but that by the early to mid teens that there was a clear difference.
So it's really not too surprising that she thinks that she can take on the PGA...she's accusomed to thinking in terms of being the best - period. She was very good at a very young age, she's dominated junior golf, and is used to being the most skilled player in her age group, regardless of gender. But now nature takes over, and the non-strength advantage that she used to having is not such an advantage any more. While (as has been pointed out) it is not so much the case as in other sports, there are definate advantages to being stronger (which is not to say muscle-bound) while playing golf.
I'll say this again: If she proves herself all the way up the line, including at the LPGA level (reminder: she's not won an LPGA event), then the next logical test would be the PGA tour. Simply put, she's not even close to being ready for this level of competition...and she appears to be wilting from the pressure.