Ahhh, but see? You're doing it. You're framing that as if his "opinion" was that vaccines cause autism. That's not an opinion - that's a belief. An erroneous one, but still a belief.
It's important to see these arguments for what they are, and how they play out. Otherwise, you lose - yeah, you may have scored all the points, but you didn't convince your friend to vaccinate your kids. We'll use two people in this argument: TNG and AVF (anti-vax friend).
AVF: Here's a link that vaccines cause autism.
TNG: Yeah, but here's a dozen that prove it doesn't, and two more to disprove the notion that your article has any basis in fact.
AVF: Yeah, but that's just, like, your opinion, man.
TNG: Actually it's not. It's a scientific discussion based on evidence, research and general consensus.
AVF: Whatever, I have the right to protect my kids.
Here's what it ACTUALLY looks like:
AVF: Appeal to Logos.
TNG: Counterargument to Logos - your argument is invalid.
AVF: Appeal to Ethos (you do not have the standing to counter-argue - note that this is a red herring that debate teams will tell you to ignore, which you did, but anyone working the art of persuasion would have had you jump on it)
TNG: Counterargument via Logos (I'm not counter-arguing, the universe is - note that you are correct but also losing... how maddening!)
AVF: Appeal to pathos (who will think of the children?)
TNG: Counterargument via Logos (the WHO, the FDA, the AMA, UNICEF and others, jackass)
The tricky thing about persuading, rather than debating, is you aren't playing for an audience. You're playing solo in a room and the instrument is also the target. The rules of engagement are entirely different. In debate, discrediting your opponent makes the audience stop listening to them. In persuasion, discrediting your opponent makes the audience (of one) stop listening TO YOU. And I can think of no faster way to do that than to say "you are not entitled to your opinion."
The response to "that's just, like, your opinion, man" is "I really don't have an opinion on this. They're your kids. They aren't in my school. Do what you want. I just wanted to point out that if you're going to entrust the health of your children to stuff you read on the internet, you owe it to yourself to read the hell out of stuff on the internet. From what I've been able to see, the guys in favor of vaccines tend to use a lot more facts while the guys against them tend to use alarmist language. Granted, the guys with the facts also tend to be dicks about it because they don't really understand how much confusion and fear plays into this whole discussion. What have you seen? What led you to believe that vaccines cause autism?"
Now we're friends again. The ethos of the opponent has been met and defused ("you are not of standing to make moral choices for my kids" - "I'm not trying to be, I'm upstanding enough to empower you to make those choices and helpful enough to help you work through it").
It's the difference between telling someone they're wrong and rubbing their nose in it and asking someone how firmly they believe they're right and then walking them back through the stuff that got them there. If you let someone realize on their own that they've made an error, they get to be the smart one. If you hit them over the head with it you're only making them feel stupid.