Paulk, my Father used to hunt with a 40 pound recurve, it was plenty for deer, also look at this quote from OL Adcock (top name bowyer) talking on longbows:
Deer, bear, and hogs, 40 to 55 pounds is plenty. Elk, I recommend over 55 lbs, and moose, as much as you can over 60 lbs.
Now I bet your sons 32 pound compound will put out about the same energy as a 40 pound longbow.
Don't deprive your son the experience when he is asking for it is MHO.