I understood it to be a self-centered statement (meant to explain, not judge). “Meaning” is something that exists in your head. You care about the state of the world because your cares are a state of your mind. Kill the mind, and there’s nothing left to do the caring.
The first objection is often “but I care about other people whom I will leave behind!” But yes, you care. Once you’re gone… there won’t be anyone left doing that caring.
By your interactions with them. Sure, after-the-fact caring won't result in any external effects, but a lot of caring is expressed in interaction which is indeed left with people. Who in turn have other cares and interactions influenced by those who cared about them. It's a chain.
The first objection is often “but I care about other people whom I will leave behind!” But yes, you care. Once you’re gone… there won’t be anyone left doing that caring.