The only thing that is impossible is impossibility.
Tautology or self-sealing argument . But only if the context of an argument. Statements like this are usually meant to communicate a deeper philosophical meaning or even irony. One might respond to that with "If by 'only' you mean 'impossibility' and countless other things such as married bachelors, square circles, or doubling a cube, then sure."
We do have a lot in common, the same earth, the same air, the same sky. Maybe if we started looking at what's the same instead of always looking at what's different... Well, who knows?
Nothing jumps out at me here as a logical fallacy without being unreasonably critical. I actually like that idea.
People's values change over time. And so do the leaders of a country. So there's no such thing as an enemy in absolute terms. The enemies we fight are only in relative terms, constantly changing with the times.
Let's put this one into logical form:
P1. People's values change over time.
P2. Leaders of a country change over time.
C. Therefore, there's no such thing as an enemy in absolute terms.
I would say a simple non-sequitur —the conclusion does not follow. Perhaps even fallacy of four terms because we are introducing "enemy" in the conclusion, which was not in either of the premises.