I debated in high school and in some ways it totally ruined me. Not really, I mean it made me a better writer (it forces you to clearly and concisely state and support your point) and a better public speaker. But it also creates this false sense of security during arguments. You revert back to your debating ways, and just assume everything/everyone else will revert with you. Your opponent will magically be knowledgeable of the subject matter and well prepared for the debate. He or she will know and respect the rules (you don't drop arguments unless you are willing to forfeit them, you use impeccable logic, no ad hominem/straw man/etc.). And in the end, you will get a bright shiny trophy or something for your successful efforts.
In real life, none of that happens. You'd think (at least!) that strong opinions would be based on a foundation of passionate research and education. But you'd generally think wrong. People are weird. And often not super educated or logical. You guys. Sometimes, I even number my arguments in online discussions (you know, to help the judge and my opponent keep track/flow the arguments). It never fails, the list is summarily dismissed. And worst of all, no matter how well the adversary got their rear end handed to them, I'm always pretty certain they walk away feeling like they made their point pretty darn well. Because generally they did make it. They just didn't defend or support it.
Unfortunately, real life isn't a debate tournament. In real life, the point isn't to win. The point is to be heard or to persuade. And destroying someone Lincoln-Douglass style doesn't necessarily lend itself to accomplishing either of those things.
First and foremost, you need to decide if you can even win the argument. Not because you aren't right and an amazing arguer. But because the issue isn't even up for debate. Off the top of my head, a few things that aren't up for debate are your personal values, opinions, and experiences. Other people can have very different values, opinions, and experiences. And they can try to discount yours. But there is no right/wrong here. I mean, I can think your opinions suck or your values are terrible. But no one can deny the values/opinions are your own. And, bottom line, you don't have to debate the legitimacy of these things (thanks, Emily). And here is a pro tip, if someone is discounting, second guessing, and pooping on your stated experiences? You are probably better off without them.
Second, if you just want to win and not persuade or be heard, then I can tell you all about using facts, statistics, and logic. Be sure to point out where they have used faulty logic and failed to address your counter arguments. But here is the thing, be aware that they will probably recoil from anything that causes cognitive dissonance (but I can't possibly be capable of not-cool stuff! I'm a cool guy! COOL, I tell you!). They will completely ignore anything that is above their head. And they will resent any feelings of incompetence that you inspire in them (and also, you for inspiring those feelings). So, while it might make for a good show and you can high five your smart friends afterwards, just be aware that might be all you're accomplishing (but sometimes that is a noble effort. I'm looking at you twitter friends who go after the science deniers/gay bashers/etc; here is a virtual high five to you. Because sometimes that effort will still leave a chip that may later form a crack that may later shatter some stupid belief of someones. Who knows. At the very least, you give me something to laugh at on twitter.)
for the record, these types of debates are kind of amazing. don't let me stop you guys from engaging in these.
Finally, just remember the other person just wants to be heard. If you just let them do that, you are more likely to be heard yourself. Or at the very least, de-escalate the discussion to a more manageable level. Something as simple as a, "So what you are saying is X? Am I understanding that correctly?" Can go a long way.
I say that from experience of not handling things that way. But (in the interest of getting the last word), I'm not good at letting people imply that my friends are immodest or don't show discretion in the way they feed their kids. I'm not good at letting people minimize someone else's humiliation or pain. And I'm also not good at letting people tell me that treating someone badly (including microagressions) is ever okay. And I'm not going to work on that. But I will try to work on having more civil debates on social media. (and/or reconsidering some of my privacy options on facebook.) So there is that.