The Kettlebell Swing, the two-hand version, is the very first kettlebell ballistic that you are introduced to in class (or at the HKC or RKC). It is also the most important of the ballistic techniques that you will learn, and such, it has to be studied and developed to a high degree. This one technique can do wonders for overall strength, endurance and body composition. Understanding how to set up, execute and recover from the Swing can greatly influence your progress in all of the other kettlebell ballistics.
Untrained or non-trained coaches/trainers/etc. make scores of mistakes when teaching the Swing. Most issues stem from an inadequate Hinge and Backswing. From there problems proceed to non-sequential locking of the joints and inadequate glute activation. Any one of these issues
Properly done the kettlebell Swing will create a dynamic and powerful posterior chain. Improperly done they will lead to dysfunction, muscular imbalances and eventually to injury.
So, before you let that person with "personal trainer" or "coach" teach you how to do a kettlebell Swing, you may want to ask where (or who) they learned how to do them.