Single quotation marks, if you recall, are used for quotations within quotations: “Stop saying ‘dude’!” They perform the same function as regular quotation marks, indicating verbatim speech or calling attention to specific words.
Like garden-variety double quotation marks, they need not curve at all. But when they do, they curve around the words they enclose. So an opening single quotation mark curves with the opening to the left, like the letter C, and a closing single quotation mark curves in the direction opposite C.
An apostrophe, when it curves, opens to the left — the opposite of the letter C. So, technically, a software program that curves your apostrophe to the right is inserting a punctuation mark you never intended.