The "science" you're referring to shows that parenting makes people less "happy" in any given moment while doing it and more "content" overall, more "satisfied" in older age. Moreover, there are significant country-by-country differences in these stats that seem to be tied to availability of high-quality, low-cost childcare and healthcare. One place to look for some overview of some of these studies is https://contemporaryfamilies.org/brief-parenting-happiness/
Probably referencing the use of the phrase "scientifically proven" and doubting the assertion being made and that there is in fact "science" that backs it up.
I think the intention is a quote rather than a scare quote.
It's a little awkward to quote a single word like that. In that circumstance the following words "... you're referring to" serve the same function. But it does highlight the notion of "you were looking for science, here is science".
