I'm not even sure it has a particularly strong effect, a quick search [0] shows that a depleted ozone would have a moderate cooling effect and a full layer would be slightly warmer but it's swamped by the effects of more direct green house gases.
Now the current and some variation of the future state of the ozone layer is definitely accounted for in the models, we just have so much more compute to throw at the modelling we can try many more scenarios but even then by [0] it looks like it's a minor effect.
[0] https://uk-air.defra.gov.uk/research/ozone-uv/moreinfo?view=...
Go back to 1950 and try to breath in LA. Go to your local gas station and ask for leaded fuel. To measure the PH of the next rain fall. There are been many environmental wins over the decades.
Your parent might mean by "we" the people who are living now, in the era when environmental concerns have become politicized, so that victories can't be bipartisan and so have become much less common. (It's inconceivable to me these days that the EPA was founded by Nixon!)
Makes you wonder if we really couldn't attempt some kind of man-made "pollution" in the atmosphere to mitigate warming.
The minor shade advantages didn't count much against the billions of tonnes of additional insulating gases added each and every year, and the decision was made to remove sulphur compounds because of the downsides of using them - acid rain and other consequences.
That said there are private groups that collecting money as credits and putting sulphur back into the atmosphere as we type .. they're here on HN and may or may not be doing a good thing.