1) not a beginners/childs horse. This person is a beginner/.child. That rules it out right there.
2) rider too large for the horse.
If you don't want to bring up the weight issue, just say the horse is not suitable. My BO and I were in a similar situation. Girl was 17, desperately wanted to ride, but weighed 300+ lb. Only horse on the farm that could carry her was an intermediate horse, which she was adamant she could handle. In short, she made a stupid decision, inadvertently cued for a canter, and being so large, she didn't have the muscle tone or ability to keep herself on. She hurt her ankle.
I'm not thin, and struggle all the time with weight, but I would never think of getting on a horse at 300# and in horrible physical shape. That's not fair, and I think people need to realize that horse back riding requires work for the person. If you want to mountain bike, be good at ballet, run a marathon, or hike to a mountain top, you have to work up to it. You don't just jump into it with no endurance, cardio or muscle tone. You don't say "I never do anything, I want to be a mountain climber, lets go climbing" and expect it to go well. You go to your local park and start walking. You research, buy the right gear, walk a few miles, then 10 miles, then up long hills. Eventually you actually are prepared enough to go for a climb.
Riding is like that. You buy the right gear, start getting in shape. It requires flexibility, coordination and core strength. You don't walk up to someone, say "hey, I know your relative, can I use your very expensive horse and tack for free while your not there?" The idea is ridiculous.