If you work in UX, it will happen to you. You'll face a situation where someone will give your research proposal a hard no. Even the small, "let's talk with a handful of people" idea you put together... no. Let's commiserate on why this happens.

We know what our users want

The most common rebuttal I've experienced is something along the lines of, "We already know what our users want" or "We know all our stakeholders. Just do this." And solely in my experience, this is almost always not true... but it can give you a firm hint of where someone's mindset is with research.

To that person, research may just mean focus groups: asking people their opinions for multiple hours, paying them money, spending a lot of time on it, and not seeing results. Or, it may mean focus groups that serve as the sole input for a project, above stakeholders and competitive analysis. In these cases, education on different research approaches is going to be a tough road but, again in my experience, is the best way to go.

Now, there have been cases where "We know what our users want" has led me to seeing a raft of research and analysis, too! And that's great. That gives me an opportunity to say, "Hey, there's a little gap here – let's talk about it" or "Yep, I agree with the findings." I value research because it continues to move design out of the realm of opinion, where people are arguing for The Thing They Like above all else.

Let's just use best practices

Fuck best practices.

Seriously.

"Best practices", in my experience, is a shortcut. It means, "I don't want to spend any time doing research." That's okay, maybe! It's totally okay. But what it suggests is a misunderstanding of what design offers: "You've done this 28 times before, so this should be easy. Just do what you did the other 28 times." I would augment that by saying, sure, I may have done this 28 times before... but I've never worked with you before. I want to figure out what's unique about you and your problem, truly. And if I can't uncover that, what I make might not fix a damn thing.

In these cases, there might not be much convincing. But talking through what "best practices" means is essential. If it really does mean "I don't have any time or money to spend", then come up with some ways to get that research and data that are cheap. If you can. If not, call it.

We know this one person, they know everything

Talking with one user and basing your decisions on that person's opinion is a bad idea. Calling it "user research" devalues that.

When this happens, it's often a variation on "we know our users". Often, there's one awesome subject matter expert (SME) a stakeholder pool knows, and they look to that person to be a proxy for users. Now, again, there absolutely are times and have been times when that person has been a proxy: they come with research, they suggest ideas on getting data they don't have, they act as solid partners.

The corollary to that, in my experience, is the person brought in for opinions only. It's a one-person focus group and because that person is so respected and known, it eliminates the worry for people. "We know this person, and they know everything, so we feel good about this." Making plans solely around this is risky as hell, because what if that person is wrong? What if they're bringing just opinions? What if they're... human?

These can be tough situations too. I still recommend listening to that SME, for sure, but framing it around additional research and context that can help get a better understanding of what you're looking to do.

How to convince someone that these are bad ideas

There's no way to do it. Sorry!

...

I kid. A bit. But here's what I've generally found to be helpful.

Education. Some people respond better to this than others, and you'll need to find how to best communicate it all, but talking through the various types of research and what you get out of it – what the value is – can make a difference.
Scale back your plans. Can't do a four-week IA exploration? Yeah, I hear you. Can you still do an online card sort to get some decent data? How about an in-person working session, or an on site day? Look for cheaper ways to get the most useful data, knowing that you're making sacrifices.
Give it time. Let things play out. Bring up questions that naturally arise due to the lack of proper research. See how it fits in or impacts your work. Make suggestions along the way.
Live with it. Not every thing you create will be perfect. Sorry. Perfect is the enemy of the good, and all that. Know and understand your personal standards on making quality shit, and make sure you're living up to that as much as possible on your project.