My wife told me is a trend to aim out of focus on portrait shot. Maybe like focus on the background and let the main subject look blurred.
Is there such trend?
What kind of photography is this?
Anyway, this photo got hundreds of likes.
I don't think there is any such trend. However, there are ways to use focus, or out of focus, to create interesting photographs. See this article at digital-photography-school.com
Some of these approach modern art for me (meh) but others are quite good. Take for instance this shot:
Or this one:
The person may be oof but they're not quite the subject, are they? The point of these shots is to make something else the subject, while using the person to add context and interest.
In the case of your portraits, try having your subject do what they love: play an instrument, sport, game, etc. Then, make the thing the subject and experiment with that.
Caution: may contain cynicism... & soft toys ;)
Is there a trend towards out-of-focus pictures?
Yes, inevitably, even if not intentionally.
As more & more people have access to photographic equipment [phones] & the ability to post the results of their efforts to social media, the eventual trend must be towards worse pictures.
Most people are not discerning over exactly what constitutes a 'good' picture & will post anything they think might be 'interesting'.
Watching someone on their phone scrolling down through their morning's social media inbox & 'liking' every other post has never stuck me as being the most analytical review of their peers' imagery.
Worse - If enough people post similarly poor images, someone is bound to consider it 'a trend' & start to copy it - though I'd have thought even the cheapest phone could have got at least one area of the shot in focus.
So... is it really a trend - probably not one that serious photographers are going to be following any time soon.
What makes it a trend at all isn't that the average person takes worse photos than they did when all people had were instamatics, it's merely that they can publish the results far more widely.
I do think there is a huge difference between pushing everything quite specifically out of focus, or moving the centre of attention by selective focus, vs simply 'getting it wrong'.
If even the sharpest parts are still slightly out of focus, as in the OP's image, then what you are left with is a bad photo, no matter what the intent. If either the flower or the near part of the rock formation had been sharp, then it would have told a different story.
A quick artist's impression - the bear & bookcase make a cameo appearance...
Below these first 4, then maybe I'll take a more serious look... but please forgive that these are all really quick examples, not meant to be 'works of art' in their own right ;)
Right click, open in new tab for larger sizes
Now, some of those may have some [small] artistic merit, but to my mind, 2 of them definitely have none - unless you're wildly interested in what types of book I read & how many of those are actually first editions ;-) 
Selective focus can be useful if you want to specifically draw attention to a feature or area not usually the one the eye would be drawn to first.
For a movie, there is a lot to be said for the reveal; starting soft, maybe backlit, then pulling to bring the hero into sharp relief...
I think this is harder to pull off in stills - but I'll leave it to you to decide.
 For the true anoraks, the entire top row that you can only see part of are all first editions, some signed