T'would have been better. But he was probably worried about recoil. Remember she had never shot a gun before in her life, and the .380 is adequate if provided with the proper ammunition. However a nice compact polymer framed .45 with a ported barrel would have been a better choice. Maybe even a .40 S&W. I've got a witness polymer compact in .45 ACP with the ported barrel, and it generates less felt recoil than old slabsides (1911A1) even though it weighs about 2/3 as much. A glock or other type without a exposed hammer might be a better choice for a neophyte though.
The only problem is for some women, a .45 is just too big around the grip frame for proper grasping. Also, a .45 is a difficult gun for most people to learning to shoot.
My opinion is: a .22 LR handgun is the best gun for learning to shoot. Then, I would consider stepping up to a center-fire handgun for a defensive gun. My own preference is for a 9mm or .40 caliber chambered Glock (provided that thorough safety training is given). The 9mm frame handguns fit my hands better than the .45 caliber handguns.
A word of caution, the 9mm handguns must be loaded with a good quality defensive load, such as Cor-Bon, instead of the economy grade ammunition loaded with full metal jacket bullets.