Pure racing boats tend to have been used hard. They tend to have more complicated sheeting. They also tend to be laid out below in a much more spartan fashion than the family wishing to learn to sail will enjoy. If you go too minimalist, and the rest of the family hates it, you'll be single handing.
Also, a true racing boat generally has a different motion in chop, or sailing to weather, and people who are prone to seasickness will (painting with broad strokes) likely have a harder time on a racer.
Finally, there are maintenance tasks needed to keep a racing boat in trim that you don't do with a cruiser or a cruiser/racer. For example, a racing J/24 will have a faired hull and keel, slick painted, which you have to haul and wash down after every race. If you don't, you'll grow a lawn on the hull. If you put regular botom paint on her, you'll have a hard time selling her to someone who wants to race. As one data point, if my family had to use the hoist every time we wanted to go for a sail, I'd be (as mentioned above) singlehanding a lot.
Many yacht clubs, at least on the Chesapeake, allow you to join up and crew without actually owning a boat. If the family gets an inexpensive cruiser, but still wants to learn to race, that's a pretty good way to do it.
Bottom line, I don't think a racing boat is the best choice for a beginner, unless they want to race almost exclusively.