Odd as it may sound, I've always been a bit too good at getting my point across.  I like toying with words; figuring out all the nuances of their meaning, taking note of cultural perception, and throwing out expressions with multiple meanings just to see which one people are the most likely to contextually latch onto. An inability to communicate isn't really a failing in our family, and for me in particular, I like my words to be surgical in their precision.
However, at the same time, a lack of linguistic ambiguity can get troublesome at times. When it's easy to be manifestly clear on exactly what you mean, it also means that if you change your mind the transformation is glaring. Technically that shouldn't be a bad thing. After all, the ability to admit when you're wrong is admirable, indicative of "strong moral fiber" and the like. But in the real world, where perception rules as king, things grow trickier.
People don't take kindly to those that change their minds. Take politics, where a track record is easily traceable, there are few things more ridiculed than a politician who has "more waffles than a House of Pancakes." Theoretically the ability to admit you were wrong is admirable, but, as soon as you descend into messy real life people don't like people that change their minds, and they don't trust them.
It's an intriguing issue. Nowadays we like songs that boast "Baby I was born this way" and "I'm never changing who I am." Consistency and conviction are strengths; indecisiveness and flexibility are the traits of snakes and liars. In "Serenity" a priest uses his dying breath to urge the protagonist "I don't care what you believe in, just believe in it."
This bothers me. I don't like people who vacillate, but, at the same time, there are few things that frustrate me more than those who refuse to explore ideas that may contradict what they think. (And when I say "explore ideas" I mean "seriously consider that there may be some truth to them, or at least make an honest effort to understand the thought process behind them." Not "grit your teeth and grouse your way through it.") Personally, I like reading articles that throw a wrench in my convictions, they force me to step back and make sure I really understand what I believe; it's my version of a morning sudoku puzzle.
When the Liberal Education movement was revived in the nineteenth century the ideal was to teach people to think for themselves. Education was no longer merely about teaching people how to read; it was about liberating men from believing something simply because someone "said so" and everybody "thinks so" and to teach them to evaluate what is and isn't true for themselves. When I hear professors talk about a liberal education being meant to give students an opportunity to "explore other subjects that they wouldn't necessarily study on their own" I want to throw a textbook at their heads. Aside from being a rather horrible selling point, it's simply wrong.
Studying the liberal arts is not supposed to be about checking out a bunch of subjects so you can discover that even though you thought you'd be a lawyer you've decided to instead get a degree in Medieval Literature. It's about learning how to learn for the rest of your life by producing a person who is "open-minded and free from provincialism, dogma, preconception, and ideology; conscious of their opinions and judgments; reflective of their actions; and aware of their place in the social and natural worlds." It is meant to teach you to have convictions because you are convinced, rather than because you are stubborn.
In the end, I think that is the way to strike a proper balance between conviction and persuasion. Quite simply, be conscious of what you believe and why, and take the time to be aware of what arguments exist in opposition. After all, "the one who states his case first seems right, until the other comes and examines him." You should believe things because you fully understand them, not because you read a rousing article promoting one side of the issue. "The false is forever in the lead in everything.  . .[and when] people marry themselves to the first tale told. . . no room is left for the truth."
In order to be a person of conviction rather than merely an obstinate one, you must have a full understanding of a matter; and if you don't, then you have no business arguing for or against it. The world of misinformation is made of third-hand accounts.
We are quick to take sides and so reluctant to part from them, but "maturity is recognized in the deliberateness with which a person adopts a creed."
Sources: JibJab, Lady Gaga "Born This Way," Imagine Dragons "It's Time," Serenity, "The Meaning of a Liberal Education," The American Association for the Advancement of Science, Proverbs 18:17 ESV, Baltasar Gracian.