This amusing poster came from writing.com
https://pbs.twimg.com/media/BTvo5UGCIAAbaz9.jpg
But aren’t you creating a comma splice by adding a comma?
I just thought it odd because of the source.
Never mind.
I see now what they are doing. No comma splice.
, and – We were warned repeatedly to avoid comma splices in my English class. “Comma and” is a common way to create one. But not in this case.
This is a comma splice, are you sure you know what one is?
Connecting two dependent clauses with “and” is called a comma splice too. Or maybe just a splice? Either way, it’s wrong.
*And *connects two independent clauses.
I just had a brain fart in the OP, and I can’t deny it. 
I saw “,and my pets.” in that writing.com example and automatically thought it wasn’t an independent clause. I had to reread it a couple times to realize they were punctuating a list of things the subject liked.
It does illustrate how hard it is to read a sentence that is missing commas.
I don’ t think ordinary readers will easily pick up what the comma is doing.
The items in the list are too variant. The list should be more consistent.
Fix that. We need to keep the action of cooking, so
“I like cooking pork and spending time with my family”.
You’re making two mistakes. The first you already caught, which was confusing the Oxford comma (aka serial comma) with a comma splice.
The second is misunderstanding the comma splice, which would be a comma without an “and”, when it’s used to join two independent clauses (clauses that could stand alone as complete sentences.)
A comma followed by “and” is not a comma splice. Often the comma is optional, but the “and” is not.
Example:
“I went to work, and I got down to business.”
This is not a comma splice. The comma here is optional (and many would say superfluous; I’d probably agree, but it’s not out-and-out incorrect). The following is a comma splice:
“I went to work, I got down to business.”
Interestingly enough, while comma splice is frowned upon, it’s pretty regularly used in novels, just to avoid overuse of the semicolon (which would be grammatically correct here).
However, there is yet another twist, when you have more than two. The following is correct:
“I went to work, I got down to business, and I got things done.”
PS: I disagree with the Wiki article’s definition of serial comma. IMHO, the Oxford comma is what that article describes, whereas a serial comma is any comma used in a series, including both commas in the quoted example directly above. Not that anyone cares what I think!
One of my proudest achievements in college was having my “freshman comp” professor (who also taught Modern English Grammar) comment on something I’d written in a paper with something along the lines of “The rules say this is a comma splice, but because of the way you’ve written it, adding a single word, even a grammatically-required and, would spoil it.”