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In the D&D 5th Edition Player's Handbook on page 195 under Shoving a Creature:

Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or [sic] check (the target chooses the ability to use). If you win the contest...

It looks like something has been omitted at the point where I wrote "[sic]" in the quote above. At that point in the text you turn the page from 195 to 196.

My guess is that it was supposed to say:

...contested by the target's Strength (Athletics) or [Dexterity (Acrobatics)] check (the target chooses the ability to use). ...

That way the rule would be pretty much identical to the way that Grappling works. Grappling is the previous topic on page 195, so it would make sense to see some close similarities.

I'm having trouble tracking down any corrections made on this particular typo, so I decided to defer to the experts. I'm looking for something official, not "it's a DM judgement call" or your own opinion. Crawford tweets are acceptable, of course.

Edit: It appears my copy is the third printing, based on the number string (9 8 7 6 5 4 3) on the first page, according to this answer. It appears this has been corrected in later printings, see answers below.

The PHB says you can use either.

Perhaps your copy of the PHB has a misprint. I checked my copy (6th printing) and it says on p195-196:

Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the abil-ity to use).

Page 195 ends after "or" and page 196 begins with "Dexterity". I included a hyphen in "ability" because the line breaks there.

I also checked the roll20 compendium which has the latest version of the PHB ruleset, and it contains the same wording as I wrote above (minus the hypen).

Misprints are common. My copy of the PHB even has a misprinted cover!

In my PHB it is exactly as you guessed:

Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use)...

Your edition might be a very early one, this change is not even in the Errata.

I have the first printing, p195 ends with Acrobatics.

You make a Strength (Athletics) check contested by the
target's Strength (Athletics) or Dexterity (Acrobatics)

check (the target chooses the ability to use).

So, it appears that a change was made that shifted the words slightly on p195. The publisher, not noticing the difference, may have used the old 196 page. If this is not an edition wide error, you may have a valuable book.