One argument that supports this conclusion is our eventual non-existence. If we all are going to die anyway, nothing we do right now ultimately matters. Our entire life does not mean anything.
To save yourself from this meaninglessness, you can Find meaning in life by attaching yourself to something bigger than you. There has to be an entity (or entities) that hold a property that is ultimately meaningful (i.e., it is meaningful by itself, it is not an instrument to meaning).