Visibility / Gusts / Crosswinds
Put...
When I'm looking to send someone solo for the first time, I am interested in all aspects of the weather - specifically the winds, crosswinds and gusts. I am also thinking about the in-flight visibility (specifically into the low sun!) and cloudbase.
I wouldn't get too hung up on forecasts - thats just what they are, a best guess. Usually they can be fairly accurate, but sometimes they can be way off the mark.
If 10 knots is coming straight down the slot, my main consideration is that the student is handling the prevailing conditions. If the student can't hack it, then I'm not risking my licence just to keep a 16th Birthday smile.
Just relax, fly the way you have been taught and if you're good enough, it'll happen. Good luck.