Say you're walking along and someone pours a bucket of water on you. That's an externality.
Say you're walking along and it starts to rain on you. That's not an externality.
From your perspective, it doesn't matter. Either way, you're soaked. Yet the former situation is inefficient and the latter is efficient. Now let's suppose that you suffer equal disutility from both situations. Then, if the nasty individual who poured water on you is made better off by doing so (why else would he have?), then we learn something interesting: in this case at least, the inefficient situation is preferable to the efficient situation. In fact, it's Pareto superior.
This kind of counterintuitive result happens a lot. If the air somewhere is smoggy and foul, that's unfortunate, but efficient. If the air somewhere is smoggy and foul because a firm is producing pollution as a byproduct of some production process, then the situation is simply better from a utilitarian standpoint, yet it is now inefficient. If someone invents a new product or a better way of making an old product and thus creates monopoly where perfect competition used to exist, the result would be a move from efficiency to inefficiency and an improvement in economic welfare.
Why do we care about inefficiency, if moving from efficiency to inefficiency can be a Pareto improvement? Presumably because inefficiency indicates an opportunity to yield further Pareto improvements. But the same is true of these efficient situations. You could yield a Pareto improvement by arranging some deal between you and the jerk with the bucket of water so that at least one of you is better off and the other no worse off, but you could also carry an umbrella. You could arrange a bargain between the firm and the people in the smog-infested area so that a Pareto improvement occurs. And you could arrange some deal between the people in the naturally smoggy area and some smog-cleaning firm so that a Pareto improvement occurs. Or you could arrange some deal between the people in the naturally smoggy area and landowners in some less smoggy area to relocate the former and yield a Pareto improvement.
It doesn't seem like there's anything special about externalities in terms of suggesting the possibility of further Pareto improvements, even in terms of Coasean bargains. It seems like problems suggest the possibility of further Pareto improvements (solve a problem, make someone's life better).
Externalities don't even appear to be distinct as a class of problems in a way that anyone involved cares about. Whether someone pours a bucket of water on you or you just get rained on, you're still wet. And the question isn't whether these costs are external or not (????) but whether anything can be done to reduce or eliminate them!
Externalities aren't even about the uniquely human interactions - for example, getting upset because you feel slighted or dominated because someone poured a bucket of water on you. People get angry at the rain for daring to pour on them when inconvenient. And people engage in market transactions with firms, getting money in exchange for being dominated by their bosses to some degree, and after being compensated for the disutility they suffer, they still get mad about being dominated.