Parents and caregivers do have an obligation to tend to the emotional health formation of their children. This is precisely why Alex referenced being a "child" as an example, in his explanation of why it would be absurd for a grown man to expect an uninterested woman to coddle his feelings if she couldn't reciprocate them.
That aside, there's a (big) difference between saying that we're not responsible for others' feelings and saying that we're not responsible for our own actions. We are responsible for our own actions; we are responsible for making an effort to conduct ourselves in such a way that others are not abused. But if someone hopes for us to give them something that they're not legitimately entitled to extracting from us, and if we don't want to give it — whether that be time, attention, sex, sacrifices, etc. — then they're in the wrong, and we have no obligation to them, regardless of the fact that their feelings might be hurt. On the other hand, if, instead of simply not giving it to them, we express our rejection in an outright abusive way, then that still lands us in the wrong. Not because we refuse to meet their emotional needs but because we're choosing to go beyond creating a passive hurt to create an ACTIVE one.
In this case, Alex knew his audience. He understood that I mistakenly believed myself to be more responsible for his emotional landscape than I rightfully was, and that this notion was holding me back from allowing us to connect better. He wasn't advocating sociopathy. He was encouraging me to drop the codependent mindset that I didn't even realize I'd been carrying.
I hope that clarifies things. Thank you for reading! :)