There were many arguments on both sides of the issue. And as with many things, there was dispute over what exactly would happen if the amendment would pass. The proponents often accused the opponents of using scare tactics, warning about things that would "never" happen. For example, from an explanation from the site About Women's History: Overview of the Equal Rights Amendment:
Among the arguments against the ERA were that it would prevent husbands from supporting their wives, it would invade privacy, and it would lead to rampant abortion, homosexual marriage, women in combat, and unisex bathrooms.Now the fight is not over, but most people believe the battle was already won: As noted at The Volokh Conspiracy:
As Northwestern University law professor Andrew Koppelman puts it, Phyllis Schlafly and other opponents [of the ERA] won the battle but lost the war: "The ERA was defeated, but its rule against sex discrimination was incorporated into constitutional law anyway, by judicial interpretation of the 14th Amendment...."Looking at the list of things the opponents were worried about (and that the proponents chastised them for), it is clear this is the case. Abortion has remained a scourge on our country, with a million little ones being slaughtered each year mostly for the convenience of the parents. Women are now in combat, and all that remains there is adding women to Selective Service (which should pretty much be automatic given the typical argument of "equal protection). And throughout the country, judges are ruling that we cannot keep boys and men out of girls and women's bathrooms, and vice versa -- for the moment, only in cases where those involved profess an identification as the other sex.
It almost seems like you might as well pass the ERA now. Given the way the current President re-defines the constitution to his liking, and the courts ignore it in favor of popular opinion, to quote a famous democrat "what difference at this point, does it make?"
But some still oppose this.