Heidegger criticizes Aristotle’s study of beings in the Physics and Metaphysics because it assumes things/objects as the primary focus. Humans (subjects, more precisely) don’t fit well into a study of beings that assumes objects are where it’s at. Plus, anything that we know, we know as subjects - in and through our subjectivity, though our perceptive abilities, our embodiment, and our cognitive abilities to think. Given this, Heidegger makes the now obvious point that should start by seeking to understand “the being for whom it’s own being is an issue “— that is us, the being that can reflect on it’s own existence and ask questions about it. We should study subjectivity and what we can come to know as subjects in the world.
Given that Aristotle made a decision to begin with objects that derailed us, Heidegger wants to go back behind Aristotle and place “humans” (more precisely human subjectivity, Dasein, Being-In-the-World) at the center and origin of his account. Heidegger names what he is doing “ontology,” using an older word to go back behind both Aristotle and Plato. As you might well know, Metaphysics is a word coined to name the works of Aristotle that didn’t fit into the Physics. Ontology, on the other hand, comes from the older word ontos (Greek word for “being”) and logos (Greek word referring to proportion and balance, that later comes to mean logic, word, reason.) Fundamental ontology is the study of beings starting from the situation of existing or being-in-the-world, later referred to as existential phenomenology.
When Heidegger’s Being and Time was brought into France, a French interpretation of the work by the likes of Sartre, Beauvoir, Levinas, Merleau-Ponty and others came to be known by the shorter name, Existentialism. And now you know, the start of the story.