Why do Southerners reffer to their relatives as Kin?

It's old English. You can start your research here: https://www.merriam-webster.com/dictionary/kin

To elaborate on what Engineer has written, cynn, the Anglo-Saxon version of the word, means quite literally, family. It also means race or type, and the words kind and child have the same Proto-Germanic root. The word has remained common for more than a thousand years, and it is not just Americans from the southern states who use it.

We wish you a Merry Christmas
We wish you a Merry Christmas
We wish you a Merry Christmas
And a happy new year

Good tidings we bring to you and your kin
Good tidings for Christmas
And a happy new year

Oh, bring us a figgy pudding
Oh, bring us a figgy pudding
Oh, bring us a figgy pudding
And a cup of good cheer

We won't go until we get some
We won't go until we get some
We won't go until we get some
So bring some out here

We wish you a Merry Christmas
We wish you a Merry Christmas
We wish you a Merry Christmas
And a happy new year

When I had to sing it at primary school we initially thought it was king, the teacher soon put us right.

I don't know why but Oliver Twist comes to mind.

Hay Boss, my cow up and died last night, so I don’t need your bull. That question makes about as much sense as screen doors on a submarine and even tho I’ma busier than a cranberry merchant in November, I’m havin’ more fun than a tornado in a trailer park.

So pull up a chair and help yourself to some victuals from the gunnysack and I’ll tell y’all what my Pa said when he asked his wife who is my sister…

‘Its a shorter version of kinfolk; meaning one's family. Someone who is connected to you by blood or marriage, i.e. your kinsman, kinswoman, kindred, relation, relative.’

However, if you upend the word (with the N on the bottom) it looks like the Korean slang word for depart hence and multiply.
Or to use the vernacular and the lowest common denominator of lingua franca; eff off.

Over here 'kin is slang for a shortened version of effing, such as 'kin 'ell.

As in the exchange between Dell Boy and Rodney.

What's the French for duck?

It's canard.

Yeah, it really is.

FYI:
https://www.etymonline.com/word/kin#etymonline_v_1860