My 2 children both started walking about the same time (15 months) but went about it in very different ways when you look at how and when they crawled, what motivated them, what kind of help they wanted, etc.
What really jumps out at me in your post though is the story you tell about this situation: describing your son as "refusing to walk" and "very stubborn." I'm a big proponent of looking beyond specific situations to your thinking about your children and whether it truly serves you or them well. The reason is because people only ever live up to your expectations of them- for good or bad. I can really see those kinds of "difficult child" labels following him through childhood and him "acting accordingly" as it becomes part of his own self-concept. Try assigning him positive qualities and intentions and watch how he lives up to those!
I think a lot of parents get into this habit and don't even realize it. If you imagine what you would like to hear your husband or a friend saying to describe you, it will be easy to get into the habit of talking about your child more positively.
Some alternative descriptions might be:
"the way my son is transitioning to walking is so interesting and unique to him"
"he is very determined and focused which are desireable qualities and will definitely serve him well in the future"
"I trust that he is learning in the perfect way for him"
"He is strong and coordinated and I'm sure he will walk on his own unique timetable"
I realize this is sort of a tangent but I hope it is of some help to you- like I said it's just what jumped off the screen at me and moved me to respond.