Some horses are resistant because they have physical problems - conformation or poor saddle fit, physical fitness, dental or other medical issues like ulcers, unsoundness or soreness - that make it difficult, unpleasant or downright painful for them to comply with our requests. Some horses have hormonal issues that can make them aggressive - mares with ovarian tumors can become aggressive. Physical problems can account for many of the most dramatic instances of resistance, and should always be ruled out first before resistance is assumed to be a training issue.
But I think that a lot of resistance in horses comes down to us - the people who have handled/ridden the horse in the past and the current people in the horse's life. Many instances of apparent resistance result from the horse's confusion and uncertainty about what we want - we may be unclear, inconsistent or ask for too many things at once while the horse is learning, leading to mental overload.
Some physical resistance - bracing on the bit when ridden, for example, or being "pushy" while leading - has just simply been trained in - the horse is doing precisely what the people in the horse's life have trained it to do by their actions or inactions.
But a lot of resistance results from horses being put into situations, often repeatedly, where the human isn't providing the horse with adequate leadership and direction. Horses know that someone has to be the leader and make the decisions, otherwise very bad things (being eaten for dinner) are likely to happen to the horse. Horses with more dominant personalities or who are very smart and more inclined to worry are more likely to quickly take over the controls if the rider/handler is asleep at the switch or ineffective as a leader. But horses really don't want to dominate people, they just want to be safe, and actually don't need to be dominated in return but are mostly very willing to accept a human's help and leadership, but, and this is a very big but, they have to feel that the human is a reliable and safe leader. If they're in doubt about this, that's where resistance comes up. The horse is saying that he isn't really sure you should be making the decisions, and that maybe he'd feel safer/better if he made the decisions for the both of you. This can lead to lots of forms of resistance, from distractability (although much of this comes from a failure of the human to provide continuous direction), to outright refusal to do what has been (clearly) requested.
Pie and Drifter are good cases in point, with very different situations. Pie is a greenie - he's only 5 and has only had a certain number of experiences in life. Things still can scare him, although he's not prone to panic - he's got a good mind and a basically calm approach to life. And, most importantly, although he's still learning how to carry himself softly and effectively, he's had a good start in life and no one has messed him up. He basically trusts people, and although he was shaken up and very worried by my fall last June (and was mad at me because I wasn't there to help him afterwards), he's willing to give people the benefit of the doubt and follow their lead. Now that some of his physical issues have been cleared away - he was sluggish and slow and stiff-moving because he really couldn't move his body until it, and particularly his shoulders, got unlocked. If you ask Pie to do something, he tries to figure out what you want and tries to do it - and no one has ever whacked on him for failing to figure things out right or quickly enough, or put him in a position where he had to make the decisions.
Drifter's a very different case. He's older - 10 - and has had several owners, all of whom I expect contributed to his current mindset. He's a much more nervous and worried horse than Pie - part of this is temperamental - his mental "thermostat" is set hotter - but a lot of it was trained in. I suspect he has experienced both extremes in the human world - some rough, aggressive, insensitive handling where he was forced to do things without adequate time to try or think them through (Dawn has had some of the same issues due to some very poor/aggressive training she received earlier in her life) - this makes him somewhat nervous and reactive, and also subsequently some very weak/absent leadership where he felt he had to take charge to make the world safe for Drifter - Heather says about him that he doesn't always want our help in working through a situation since he's used to having to do it himself.
Hence Drifter's resistance. Heather and I have trying to work through this with him, and it's taking some time - this is why he's staying at her place through April - because even when the overt physical resistance is eliminated, and he tries and succeeds in doing what is asked (and he really appreciates praise and isn't aloof - he's a very people-friendly horse), there's always a feeling that he's still doubting you on the inside - he's holding some part of himself back. So he's the paradox of the horse that can be apparently soft on the outside, moving well and compliant, but isn't soft on the inside - he's not "with" you emotionally even if he's there mentally. This also leads to some inconsistency in his work - that underlying emotional resistance keeps resurfacing, and asking him to do something more or different can arouse his doubt and his learned resistance patterns. He's holding back because he just isn't sure that he should hand over his trust . . .
A little like peeling an onion . . . we'll get there with time, and Heather is doing a fabulous job with him. He's slowly starting to thaw . . .