Why does Sartre say “I cannot make liberty my aim unless I make that of others equally my aim.”

I’m fairly new to existentialism, so I’m genuinely curious about this and would really appreciate being corrected if I’ve misunderstood Sartre. In *Existentialism Is a Humanism*, Sartre seems to argue that because there is no predetermined human essence or external moral law, we are radically free and responsible for creating ourselves and our values through our choices.

But he also says that “I cannot make liberty my aim unless I make that of others equally my aim.” What exactly justifies this move? If existentialism begins from the freedom of the individual and rejects an objective, pre-given morality, how does Sartre get from “I recognise and will my own freedom” to “I must also will the freedom of everyone else”? Is he saying that recognising myself as a genuinely free subject logically requires me to recognise other people as equally free subjects, or is this an ethical commitment Sartre introduces on top of his account of freedom?

And if I simply chose to value my own freedom while denying the freedom of others, what within Sartre’s philosophy would allow him to say that I was mistaken rather than merely choosing a different set of values? I’m new to Sartre and existentialism generally, so please correct any assumptions I’ve gotten wrong, I’m genuinely trying to understand the argument.