You do need a comma before a conjunction if it connects two independent clauses.

So it's "You do need a comma before a conjunction, if it connects two independent clauses" then — "you need a comma before a conjunction" and "it connects two independent clauses" are two fully formed simple sentences, each having its own subject and predicate. See what I mean?

And almost nobody writes sentences like "I love her and she loves me back" with a comma before "and".