Well, this answer isn't really as specific to programming as you might think. You have to bring it back to things they do understand.
If it's something like composition over inheritance, you probably just have to say that currently perhaps 90% of developers would consider that a best practice (a wild guess, based partly on the fact that 100% of developers agree on almost nothing), and you agree and would be happy to go into why.
I try to be as honest as I can about what's controversial, and what percentage of developers would agree with me.
This generally works better with management than developers, who probably will make you go down the rabbit hole of explaining whether you are really advocating good design and how do you know it. There is something commendable in this, but it means you must put a lot of time in. Unless they trust you enough to take your word for such things, at least provisionally. On the good side, they may convince you that you are wrong, which beats cold, hard reality convincing you down the road.
For things like a design being more testable, if they don't agree that it is more testable then it's pretty much the same as the first example. If they don't agree that it's desirable to be more testable, then you have to bring it back to things they understand. This would most likely be management, and you can talk about lower development costs in the long term, less QA, more predictable processes (since the length of repeated QA cycles is hard to predict), etc.
I think part of the problem is that you underestimate how difficult it is to get a team to agree with you on anything controversial, even if you happen to be correct (and of course you may not be). Programming is partly a sociological exercise and you may need to schedule time to actually go down some of those rabbit holes, since a great design that no one understands or gets behind is rarely a great design in practice. So don't think of that time as wasted, think of it as a necessary part of your project's success. Even though it would be so much easier if you could somehow skip it.