Why do some tv news programs refer to age as 10 years his junior?

Because they are emphasizing that he is much younger I guess. Sometimes things like this are just colloquialisms. Customary ways of saying something where they are from.

Normally they give the age of one of the person’s at some point in the program, than you can figure out the age of the other. Ex. Jane Doe age 16 was 10 years his junior. (Meaning the other person was 26).

A stylistic choice, IMO. Less redundancy, more focus on the difference in age.
It’s one of the little ways that the media distorts your perception of the facts.

The sake of seeming sophisticated..?

For describing something of a statutory nature for effect, hoping people can subtract ,and after working on the computation makes the point seem more relevant since by then they some time invested.

It’s not a TV thing. It’s simply a way of referring to relative age (that is, the age of one person in relation to the age of another), both in speech and in writing. Some TV scripters are making use of this existing convention just as they might use any other established expression as a way of conveying information.

Because when they do this it is usually a old dude banging a younger lady. And we all know how woman react when you say their age.

ducks

Partly it’s because they don’t expect people to be able to do the math in their heads, but mainly it’s to point out what are (to the reporter) the most salient facts of the story. If you say that “Mr. Smith, 57, and Mrs. Smith, 47, are having their first child”, then people have already zoned out on how old Mr. Smith is (they weren’t listening, because it wasn’t critical to them), so they 1) don’t remember how old he was and 2) can’t always think fast enough to do the math in their heads even if they did hear his age and 3) having the listener do mental math takes his attention away from the story.