Principles of behaviour have to be understood in context because what is good for one occasion may be totally wrong in another. In the context of following Jesus in order to become like Him, Jesus said that we need to deny ourselves, die to ourselves daily in order to do His will (Lk.9:23). Two wills come in here, that of God and ours. Whenever they are in opposition, we have to deny our own will. We give it up happily because we are getting a better deal by doing God's will. Our will is usually associated with sinful desires, and if we want Jesus to save us from our sins, we need to humble ourselves, put aside our will and do what He tells us. This is 100% right because Jesus is always right and always doing things for our eternal good.
But this doesn't mean that denying ourselves is the all-time path we follow in every area of life. Should we always give in to every person we meet? It doesn't even mean that we should always give in to everyone who has some authority over us. No human being is perfect even when they are anointed by God! We ought to have an attitude of submission towards them, and obey them whenever they want us to do something within their area of authority, even if they are somewhat unreasonable (Ep.6:5;1Pe.2:18). But we don't have to let them lord it over us to the extent of wanting us to go against God's ways or our conscience (Ac.5:29).
If some 'strong' spiritual leaders 'demand' an unquestioning submission to them, beware! A few such leaders can't even tolerate a difference of opinion on their biblical interpretation or ministry. We mustn't think that because they are 'anointed' by God they are to be like God to us. They too are only men and are imperfect in their understanding and knowledge. If we blindly keep submitting to them we won't be able to fulfil God's calling for our own life. It is sad to see people who seem to have thought that 'submission' is the way of humility and have become powerless yes-men having lost their own potential and unique identity.
We see many wives 'submitting' to their husbands even when husbands are abusing them harshly, effectively becoming the platform which supports such abusive behaviour. They don't even want to seek help from others, because they believe it is their duty to just submit always!
Always submitting may look like humility and godliness. But it's not always. Look at how Jesus behaved, taking the form of a servant in order to fulfil the Father's will even in death, and yet not cowing down before Herod, Pilate or the Pharisees (Php.2:6-8). He was thus able to fulfil His purpose in life.
It's not to promote pride or rebellion! It's just that people are all imperfect and that our dealing with different ones must be based on what is godly in that situation. We mustn't follow just one rule – humble yourself. Remember, there is a time to answer a fool and another time not to (Pr.26:4,5). Sometimes we have to disagree with men in order to obey God.