最近、結婚しない人が増えているって英語でなんて言うの？

This is a way to state in American English that throughout the last ten, twenty, or even thirty years, that people are not choosing to get married as much as people previously did. This is a comparative statement that allows you to have an opinion about the rate of marriage throughout the years.

I hope this helps :)

"Today" can be used to refer to the present period of time. For example: "today's society."
"Lately" is used to refer to events in the recent past or situations that started a short time ago.
"Prefer" means tend to choose.

It is an old phrase, but the actress Cameron Diaz recently stated that marriage was a dying institution.
It seems the option of marriage is less in vogue than previously in our history. And of course, of those that do marry, the majority of those marriages are, unfortunately doomed to fail.

If something goes up then this is called to 'rise' or to 'increase'
When talking about something that has happened not that long ago we use the term 'recent/recently' when talking about this in years we say 'in recent years'
If you make your mind up about something you say you have 'chose' or 'decided'

"These days, more and more couples are choosing not to get married." - This is an alternative way to say this same expression especially if you are referring to people in a relationship but are still not getting married.

"Remaining single is an increasing trend." - This example explains that more individuals are staying single according to recent statistics.