I've noticed this phrase being used a lot following the news about Texas. I'm pro-choice, and I don't think it helps our cause.
There are women who have abortions lightly. It's not a myth started by the Daily Mail. I don't even think it's necessarily even that rare.
There are women who actively want a baby in the near future, are in stable relationships, aren't even using contraception, but still decide to abort because the timing isn't 100% perfect: they don't want to cancel their holiday abroad, or give birth until the extension on their house is finished. Trust me, it happens. Does anyone really think those women agonised over whether the holiday/extension was more important than the baby, before painfully including that abortion was the only option? Of course not. And that's fine. Women shouldn't have to ask if their reasons for aborting are "good enough".
Then there are the women who are on their fifth or sixth abortion - workers at abortion clinics will confirm that this does happen. It seems unlikely that those women agonised over their decisions either, because presumably they would have put some long-term contraception in place to stop it happening again. I expect most of them come from pretty traumatic backgrounds, but that doesn't mean their decision to abort isn't made perfectly casually.
This phrase is a gift for pro-lifers, because it's so easily disproved: many of them will have stories about women they know who've had abortions without a second thought. A better argument would simply be that it doesn't matter why a woman wants an abortion: she should be allowed one because it's her body and her choice.