The grip you use should match the overall style of the game you intend to play. For youngsters, this is a strategic choice intended to maximize their potential once they reach their late teens.
You should ask the pro, "why" he wants her to use an Eastern grip, and then decide if you trust his choice of strategy. You might want to get several other opinions from other pros to see if there is a consensus.
Western grips allow you to impart more topspin onto the ball, but that diverts energy into the spin of the ball and away from velocity. It's really nice to have both shots available to you, but most people become good at one or the other. Some coaches prefer young players to start learning their weaker shot, knowing that in a few years they can switch to their more natural shot, leaving them with two skills instead of one. Other coaches think it's better to focus on the primary shot immediately, and thus maximize it's potential. That's why I say this is a strategic decision which needs to be matched to the players ultimate style of play.