I know individuals who are perpetually locked in battle with someone over something. Having been one of those people, I know how exhausting and frustrating that mode of operation can be. We really must consider the intelligence of engaging in a siege against someone who has already made up their mind about what they believe and determine if that is an effective use of our time and sanity. No matter how right you are and how wrong they are, when someone has made up their mind, attacking them head-on is just another version of the irresistible force vs. the immovable object.
If destined for protracted battle in the case of trying to change and the change is necessary, timing is essential. We must enlist allies and create strategies for change. And then, when the timing is right, introduce your well-thought-out argument without being emotional or threatening. Allow the other party to come to their own conclusions and they will often come willingly. This is, of course, what is termed as "buy-in", but sometimes we don't see it quite like that from the other side of the table.
Some people, however, no matter what, can not be swayed by logic. They are so emotionally tied to a belief that no matter what you present, they are entirely convinced you are wrong and they are right. I see the constant "conspiracy theorists" at work in society daily, not just in the workplace, but in political and religious discussions in which one or both parties are absolutely unwilling to see another's point of view. If you find this to be the case, even Sun Tzu advises, "besieging a walled city is to be the tactic of last resort".
Even if you strongly believe you have all the reason in the world to be in the right, when you are facing someone who is deeply entrenched, we have to understand that if you can't make it safe for them to come out from behind their defenses, they won't. And if you have ever tried to open a closed oyster with your bare hands, you can probably guess that changing their mind is going to be a lot like that. Ultimately though, if you have exhausted the alternatives and tried to use a shared mission and legitimate reasons to work together, there are two ways in which to attack a siege: by surrounding the fortress and waiting it out, knowing that at some point the occupants will have to weaken their defenses to get sustenance, or employing a siege engine.
I can write volumes on the use of overwhelming a siege mentality, but the basic thing is this: doing so requires considerable resources in the aspect of time and patience. And when you are done, there are often lots of casualties on both sides, the casualties sometimes are just innocents who happen to be caught in the crossfire, and there is sufficient collateral damage to both you and to the opponent that "breaking a siege" must be considered a last resort.
Consider your strategies and don't just rest what seems to be the obvious alternative. While trying to get someone to come to the same place you are may be frustrating and time-consuming, realize that utilizing a siege engine is not going to be clean and there will be plenty of reasons you will regret having used it later. But in some cases, that truly is your only option, and when you use it, you'd better come prepared for war.