Crisis on Infinite Earths ran from 1985-1986, a massive universe(s)-wide crossover that rebooted the entire universe, radically rewriting some aspects of DC history. One of the major changes was to the history of Superman and Batman's relationship, which was shifted from chummy to antagonistic from the very beginning.
World's Finest was canceled in January 1986 as CoIE drew to a close. The last issue featured a mournful cover, but the exchanges within are anything but, as Batman chews out Superman for needing him to save his life and basically announces Clark has gotten too dependent on Batman and so he won't team up with him anymore.
You can read the key pages here.
Frank Miller's
The Dark Knight Returns #1 was published the next month. The timing might not have been deliberate, but it also was no coincidence, as Miller's Superman-Batman dynamic came to replace the traditionally friendly one of the World's Finest title. To understand what happened between Clark and Bruce between 1986 and about 1996, it's necessary to look to a future AU and its effects on the past.
Frank Miller (perhaps pissed off after reading "A Kryll Way of Dying" two years before), set The Dark Knight Returns in the future of the DCU, portraying Clark and Bruce as former friends who have come to be bitter enemies due to political pressures.
The mini-series had a gripping, vital energy to it, and Miller's vision of Superman and Batman as angry old foes sent shockwaves through the comic-book fan community. It was interesting, dramatic, and different, and it drew a bright line between two characters, making them more distinct. As a result, the antagonistic image Miller had of the future ended up affecting the way people wrote them in the present.
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Read more of Dark Knight Returns here)
The shift is clear from the very beginning of the rebooted universe, in John Byrne's "Man of Steel" miniseries released in Nov. 1986. In that miniseries, Byrne wrote the "official" version of Superman and Batman's first meeting. Batman tells Superman that if Superman lays a hand on him, it will trigger a bomb that will kill an innocent person. Superman is appalled, but reluctantly works with Batman to solve a case; at the end, Batman reveals the "innocent person" who would have been killed was Batman himself, and Superman grudgingly agrees to leave Batman alone. (
click to read some scans from "Man of Steel")
In the post-Crisis DCU, Superman and Batman are no longer on the League together; as a result, with their team-up title canceled, the two interact less and less. This allowed the DC writers to more clearly delineate the two, placing them in very different worlds, with two very different worldviews. Post-Crisis, Superman was no longer on the Justice League, but Batman was again, in what has come to be known as the Justice League International years with (among many others) Booster Gold, Blue Beetle, Mr. Miracle and Barda, Fire and Ice, and Guy Gardner. Thus, Superman and Batman very rarely interact, and when they do their conversations tend to be terse and businesslike, with the two of them talking past each other, like they're almost speaking two different languages. One of those rare interactions happens in Justice League International #19 in November 1988: here's the entire exchange between them.
However, even if Clark and Bruce don't like each other much during this time, they still trust and respect each other. A good example of this takes place immediately after the JLI scan above, at the end of
Death in the Family (Dec. 1988-Jan. 1989), the story arc in which Jason Todd is killed by the Joker. In it, Superman is sent by the US government to prevent Batman from killing the Joker, who is now the United Nations ambassador for Iran and thus has diplomatic immunity. The two of them repeat some of the same arguments about law and justice that first appeared in the Batman and the Outsiders origin, but once Clark realizes what happened to Jason, his attitude toward Bruce changes. In the end, Superman leaves Batman with the Joker, either trusting him not to kill the Joker, or giving him tacit permission to (most likely the former, of course, but it makes an interesting parallel with a similar conversation in Jeph Loeb's Public Enemies story arc in 2003, in which Batman says he's okay with Superman killing Lex Luthor).
Similarly, in a three-part story called "Dark Knight over Metropolis" (June 1990), a reluctantly teamed-up Superman and Batman snipe and bicker a lot, and Superman goes so far as to say "I'm not in the habit of barging in on friends unannounced, but then, we're not exactly friends...are we?" (*sighs and misses the old days for a moment*) However, this is the storyline in which Superman gives Batman that Kryptonite ring, the ultimate symbol of his trust. So even though they're not interacting often, and even though both would be quick to announce that they're not at all friends, when it matters they see each other as equals, worthy of trust and respect.
However, things can and do get even worse between the two of them. They never become openly antagonistic as in Miller's vision, but DC drives them even further apart starting in 1990--not by having them quarrel, but by simply having them not interact at all for four years.
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