The Pen is NOT mightier than The Sword
Throughout my life, I've heard two phrases which never really made sense to me. Both of these glorified the notion of abstracts and human values transcending us mere mortals and heading on to become immortally set in stone. One of them goes like this:
The pen is mightier than the sword.
In my own opinion, this simply over glorifies what words can achieve over what we can do as the animals that we really are. The other goes something like this:
Ideas are bulletproof.
Your ideas are temporary. No two people can have the same idea, and to propagate it is a different task altogether. Allow me to put forth my arguments in the following sections.

Writers and their fragile Egos
There is something about writing which causes people to lose their sense of humility and gain a sense of pride and arrogance which they use to challenge Gods and put forth words which aim to put them in a position of power. Simply put, they prefer to use words and appear larger than they really are. No matter who it is, every writer strives for a sense of control over the readers, and listeners and there comes a point where just engaging them is not enough. They must influence them and sway them with their words. They want to control the minds of their readers, and that in turn breeds in them, a sense of arrogance. They end up yearning to control others the only way in which they can: by using big sounding words, deceit, and a lot of misdirection.
They simply want to gain the power and influence which they never found as writers. It's like a drug that begins to control them. They crave control of others when they see they have the power to influence them. It's not their fault, really, but what they resort to isn't correct either.
You can read more about how ego influences art in this article by @sams-world.

How there is immense power in the Pen
The pen. A metaphor for the power of words. Do not be fooled, for even words do, in fact, hold immense power to sway, influence, oppress, or even scar. In fact, it is the same power which many writers inclusive of Shakespeare, J.K. Rowling, and influential speakers such as Mahatma Gandhi, and Adolf Hitler among many others use and abuse. The people fluent in the art of words use its power to their own benefit to meet their own ends. The same power also comes in handy for most businesses, societies, politicians, and criminals. However, there is a limit to such power. Let us explore all that words can do.
Words can, in fact, achieve what the sword cannot, for words can also make in addition to breaking, but the sword can only break. Words are, like most other things available to Man, tools to be used. In what manner they are used, rests solely upon the wielder of the tool. It can be used as medicine for the soul, or as a weapon to cut them down.

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Words can be used to inspire hope amongst millions and millions of people to break free from their chains of oppression, as in the case of Mahatma Gandhi, or Nelson Mandela. On the contrary, Words can also be used to instil hate among an entire nation against certain others, as in the case of Adolf Hitler.

Words can be used to appreciate someone and raise their status in society. On the other hand, words can also be used to drag someone's name through the dirt and make them a symbol of shame. In fact, that is what most media thrives on in the modern day. They can cause a sense of trust strong enough to make people lay down their lives for the subject, or a sense of fear and hate strong enough to make hunt and kill the subject.
Words are especially useful while shaping the society. They aim to nurture the young ones and shape them into a certain way of thinking. Education is based solely on words, and it is particularly effective in the fact that it can shape the young and growing brains into the way intended, and more often than not, that way remains the same throughout their lives. These are all things which the sword cannot achieve, but words can.

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Where The Sword really triumphs over The Pen
Words may hold immense power, but like all things, they too have a weakness. Words are only as effective as the extents of humanity go. Words can make or break, but only that which is human. For all things inhuman, we have The Sword. A metaphor for any tool reserved for the sole purpose of killing. Quite ironically, what is so inhuman and relies on such inhuman means, also rids us of our humanity. Both the person who is struck dead as well as the person who strikes him down. Essentially, all we are is just Monkeys with wild and vivid imaginations and methods of play. In being inhuman lies our true nature.

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Words can hurt someone emotionally. They can inspire someone, or make them feel like they aren't worth anything, or can never be worth anything. It can break their self-esteem, and it can make them regret living their life for the rest of their numbered days. However, the simple solution to that is to hold your own and stop caring about what people think or say about you. That is all there is to it. All effect that words can have on a person are directly reliant and dependent upon the person themselves. Words will stop getting to you if you just don't let them get to you. The power of pain and pleasure is all in your hands. Blessed are those whose lives are so devoid of tolerance, that they are hurt with nothing but mere verbal statements.

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As far as shaping the society is concerned, it can shape the society however it wishes to do so. The pen does emerge victorious in this scenario. However, all it takes is a couple of free thinkers to break free of all their education and programming. From there, it is upon them, whether they start a revolution, or they live their own lives in peace. As far as society is concerned, a place does not deserve someone who it cannot welcome.
Those who argue that words can cause permanent psychological damage are indeed the mentally weaker people. Mental scars can heal completely. All of it is in your hand. Your brain can rewire itself any time, and it all begins with your personal effort. It takes time, but all mental scars and wounds heal permanently until the time that they no longer hurt. The same cannot be said about physical scars. They take time to heal, and the pace is not in our hands. Not only that, they never heal completely. All those who say that emotional scars are more painful than physical ones have never been set on fire.

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The sword, on the other hand, can do much more than simply deny you the pleasure of hearing compliments for the rest of your life, or drowning your name in a pool of mud. All our humanity ceases to exist as soon as our heart stops beating, and all the life has been drained from our body. It does not matter whether you use it against a king or a slave. It doesn't matter whether or not the other person cares about it. The only rule with the sword is, the one who remains standing is the one who is victorious. All your human fame, name, money, emotions, belongings, experiences, pleasure, pain, all of it ceases to exist when you are cut down by but one swift stroke of the blade. You cease to exist.
If the pen was indeed mightier than the sword, then we would have authors and poets fighting wars, and not soldiers and spies.
Ideas are as temporary as the vessels that carry them
A lot of people claim that ideas are bulletproof as if to entertain a school of thought that ideas are in fact, something immortal, which shall transcend the bounds of mortality and continue on beyond us humans. However pleasing that may sound to the ego, it is in fact, untrue.

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All ideas belong to humans, and they shall remain there as long as the humans who hold the ideas have died. Once the humans which carry these ideas are gone, the idea can only remain in other mediums, all of which can be easily destroyed or contained. Books can be burned down. Stones can be broken. Pictures smeared and ruined. And all humans killed.
When it comes to the sword, all the powers of the pen fade away. In the end, the true laws of nature always emerge victorious over all our human tendencies, desires, and egos. Nature has only one law: Survive or perish. The pen is indeed quite mighty, but to say that the pen is mightier than the sword is not only incorrect, but proves to be a rather arrogant statement. The pen can hurt all things human, but the sword can do much more. Words and ideas are not the end of the world. But for any individual, death surely is, and that is exactly what the sword deals in, and the pen doesn't. To be exact, the pen shall never hold enough power over the sword.