congrats on starting a new sport. If the horse if frequently used for lessons and ridden by a lot of different persons he may have become somewhat dead to the aids. He will be slow or stubborn as a way of protecting himself. Also, because he knows he can get away with it. If the teacher couldnt motivate him then maybe , just maybe, he has a physical reason for not wanting to jog. Prbably not, tho. He probably has had so much time with beginners on him that his mind is tuned out and it took a fair bit to get him back "awake" again.
When you are starting a very calm , even lethargic horse like this is not such a bad thing. Once you feel more secure in you saddle, you might as if she has a horse with more go. Learning to ride takes more time than most people think. You have to train your body to do somehting that is totally new to it, and if you're an adult when starting, it's even harder. But boy is it fun!!!