What can I say to my friend (spouse or parent) to encourage them to attend strength and balance training?

There are many benefits to attending strength and balance training and it perhaps is not necessary to mention to them that attending training is good to prevent falls. You could talk about the many other benefits of strength and balance training, such as feeling good and maintaining their independence. People get a lot of enjoyment out of attending, particularly the socialising aspect. You can assure them that it would not be harmful for them.