You cannot derive an is from an ought, and you cannot derive an ought from an is
What do I mean by that?
Is - is referring to the state of reality, we live on planet Earth, writers write, jumping off of buildings is dangerous, etc, etc.. These are all descriptions of reality. They are telling us what reality is.
Ought - is referring to the state or reality we would prefer, you should be good, you should not lie, you should help others etc, etc.. These are prescriptions of reality. They are telling you what reality should be.
To distinguish one from another is to distinguish fact from value, the fact-value difference in epistemology.
Essentially - you cannot claim that you should do something because something is the case. Why? Well, because that would assume the goal. Or the direction of the morals, there is no link between the specific moral claim and the claim of reality except for your own subjective take. However, if you were to include another ought in there, well, perhaps I should explain in an example.
P1: Biting another person hurts
Con: Therefore you should not bite other people
That is a non-sequitur, the conclusion does not necessarily lead from the premise, what if someone finds pain enjoyable? Therefore the accurate syllogism would be as follows:
P1: Biting another person hurts
P2: people should avoid pain
Con: Therefore people should not bite other people
Do you see the difference? The second premise is something that changes the validity of the conclusion.
While it could still be the case that some people don't avoid pain, or shouldn't avoid pain, it makes the argument a sequitur, where the conclusion follows from the premises.
But how does that lead us to morality being subjective?
Simply put, that second premise simply cannot be based on a fact of reality, there is no link, and the conclusion can also not be based on a fact of reality, at every level there is a preference, or a goal inserted to make the syllogism valid. It is literally impossible for a moral ought to be based on entirely factual things, there has to be a prescription of which facts are preferrable and which aren't. This is the subjective nature of morality.