Liberal and Conservative
As a native English speaker who's bombarded with coded political language every day, I know which constellation of words will inevitably appear on the website of a conservative group in the contemporary US context, and I know which ones will appear on the website of a liberal group in the same context. (Or in their written statements, or in posts by people from either of those two stripes.) "Tradition, values, freedom, personal responsibility" = terms used exclusively by the Right. "Diversity, tolerance, equality" = only on the Left. "Respect, individual, dignity" = used promiscuously by both, either because that's what we all *really* believe in, or to obfuscate differences. (And funny that the French motto includes one from the Left and one from the Right, plus the ambiguous "brotherhood"; but I think this will prove significant later on.)
But what always strikes Lefty me, is how the right wing catch phrases or pet words aren't ones I dislike or disagree with. Perhaps those on the Right could even grant that they have nothing intrinsically against "my" words. And let's try to step past the accusation of insincerity, as in, "Sure, they say they believe in freedom but they don't really!" or "They only believe in freedom for themselves!" I think that's too cynical. I really don't believe all conservatives (in either a political or intellectual sense) are intolerant or believe people should be treated w/o equality (though of course there are demagogues who do use rhetoric to mask what they really believe). Again, I'd hope for enough tolerance from my friends on the Right that they do not think I favor enslavement and I take no responsibility for my actions. Again, these would all be caricatures and we'd never have dialogue if we believed in them.
What I really believe happens (demagogues excepted) is a conflict in the ordering or prioritizing of goods, as well as disagreement over the public and private elements w/in those goods. In other words, to me, "personal responsibility" is crucially important in my life, but was taught to me a very long time ago and mostly in the private setting of me being raised by my parents; so I don't see that as a point of my identity I'd need to advertise or use to define myself, as it's nearly instinctual to me (though there is also a temptation to violate it, it would still be done w/ full knowledge one had violated something one holds dear), and requires neither education nor debate nor public funding; I take it as nearly axiomatic that all people were taught that at a similarly early stage. I really don't see it under attack, the way so many people on the Right do. Of course, they don't see "tolerance and equality," as threatened, whereas I do, because I was only taught to value those much later in life and they relate to a much more extended society than my friends and family, people to whom I feel less natural affinity.
Or really, to put it another way, I think it does come back to the two terms we've taken from the French motto and throw around so much in our current rhetoric. I think everyone on Right and Left could agree with this: Humans naturally desire freedom (though I'm using the term uncritically, let's just go with it), but they don't really desire equality all. (Everyone I know wants to have MORE than other people, not an equal amount.) Lefty me believes in greater protections for equality, because it is the less likely for people to pursue on their own (and at the extremes of inequality would threaten freedom). People on the Right see that as limiting freedom, which they think, since it's the more natural and universal of the two Goods, should not be impinged on at all. For them, protecting freedom is all you need, and whatever level of (in)equality you ended up with among free agents would be fine (or, at the least, necessary and unavoidable and not worth threatening freedom over). To me, they have reified the value of Freedom over everything else; to them, I'm naively and misguidedly pursuing a "good" that is not natural (equality) and must be forced on people.
Unfortunately, although that may clarify some things, I don't think it makes dialogue any easier (since it boils it down to a more fundamental disagreement over values).