(Edited to be more clear)
One can find plenty of witty advice catch phrases that appear to be in direct conflict with each other: "Early bird gets the work, but the second mouse gets the cheese" (from a comment below)
You can also find this with things that are more detailed frames than cliche advice. One that I've been mulling over is "decision makers need skin in the game to not be act stupid" and "asymmetric justice (people being punished for messing up) incentives inaction."
The "quality" of any advice varies wildly with what you are trying to do and what your specific context is. It's not going to be the case that the "best" thing for everyone to do is either follow the mandate of "have skin in the game" or "avoid asymmetric justice". In fact, you might be thinking about ways that those to ideas aren't even really at odds with each other. Yet my personal experience was hearing about skin in the game, going "that sounds obviously important", hearing about asymmetric justice and going "this sounds obviously important", and later in a conversation with a friend going, "Wait a second, my low resolution understanding of these ideas puts them in direct odds with each other."
I've learned a bit from hunting for pairs of advice/principles that both sound like good ideas to me, but at first glance seem to be at odds. Then exploring "why do they feel like they conflict?" Sometimes I find that they don't actually advise completely different approaches. Sometimes I find that each piece of advice is paying attention to a different dimension of trade off, and that conceivably I could do well by paying attention to each dimension separately.
I'm inviting people to use this post to document paradoxes you find in your own thinking. Explore where the sense of conflict comes from, what there is to learn from each side of the, what a synthesis might be, or when one might apply more than another.
Don't feel like you have to solve the whole thing, just try and unravel the problem space a bit.