Freud is simply going to inevitably come up at some point in a psychology degree, because he's had an obvious influence upon the field of psychology in a variety of ways. In a similar way, a colleague in the psychology department I teach in once asked me, 'do you teach anything about Jung? I feel like at some point we should cover him across the course of the psych degree, but if he's not in your class, I don't think we cover his stuff at all.' (I do have about 10 minutes in one lecture about Jung - phew!). And that goes to the heart of Freud - he's such an influential figure in the history of ideas surrounding psychology, he's one of the psychs that people have heard of, and so psychology students probably need to know who he is, if only to explain the differences between Freudian psychology and most modern psychology.

Additionally, very often within psychology classes (or books on a topic) he is treated in a very Whig History kind of way. Whig History refers to a kind of history that mostly treats things in the past as steps on the road to greatness, where the things in the past are seen primarily for how they led to our current (obviously, quite brilliant) state of knowledge about the world. Whig History is a problem because it typically doesn't present the thing in the past as how it was, but instead treats it in a way that is very filtered through what it added to our current understanding, and also therefore what it got wrong (but often without much context of why the theory was the way it was). Whig History is particularly common where a scientific field is telling its own history in a textbook or lecture or so forth; this is because the historical stuff in such classes are usually a way of showing how the current way of thinking came to be, and by proxy what the current way of thinking holds to be most important, which are illustrated by comparing the current way of thinking with the ye olde previous way of thinking; in other words, they're largely teaching you about Freud because they're really trying to get you to learn about, say, CBT or modern cognitive developmental theories. They're also likely teaching it in such a way that you end up thinking it's not a great theory, because they probably want you to think a different theory is actually the better theory.

This also means that, when it comes down to it, you're probably not getting the full picture of Freud's thought in context, and the focus is often on what he got wrong, rather than what he got right. Broadly speaking, psychology as a science is indebted to Darwinian evolutionary biology for its existence, as in the 19th century, evolutionary biology paved the way for thinking that human minds were part of the natural world, and thus we could find things out about them through scientific methodology. Out of the people in the late 19th century who thought about the implications of Darwinian evolutionary biology on human psychology, there were a bunch of different approaches, but Freud is the one who tried hardest to construct a general theory of the human mind modelled on Darwin's theories of natural selection.

Perhaps inevitably, his theories are limited by his frame of reference in middle class turn-of-the-century Vienna (just as much modern evolutionary psychology is limited by the characteristics of the undergraduate students who make up most of the participants in their experiments). They're also limited by the limited understanding of evolutionary biology at the time; for example, Freud was writing well before the discovery of DNA, and his understanding of evolution comes from Ernst Haeckel's writing rather than Darwin, and there are Lamarckian aspects to the way that Freud thinks about evolution that are very outdated today.

But nonetheless, Freud did try to construct a general theory of the mind that's fundamentally evolutionary in nature, and it's simply the case that if the mind is evolved along the lines of Darwinian evolutionary theory, then the structure of the mind is very likely influenced by the processes of natural selection and sexual selection (Darwin believed that animal behaviours have evolved because those aspects of behaviour are more likely to result in that animal surviving and reproducing). But Freud had a problem: while, according to Darwin, our minds are likely to be evolved, and likely to be therefore structured around survival and reproduction, our conscious experience of our minds seem not to be structured around survival and reproduction: we write books, we look at pictures of cats, we play sports, we do a bunch of things that are not obviously about survival and reproduction. Freud's solution to this, of course, is the unconscious: if the things we do aren't consciously about survival and reproduction, then they might unconsciously be about survival and reproduction.

Freud's developmental stages are, therefore, structured around how we turn from a screaming infant focused entirely on survival to a functioning adult member of a society where men don't just, you know, get out the penis at every opportunity (apart from in cases like, I guess, the recent event where Jeffrey Toobin apparently failed to suppress such urges). So things like the phallic stage are part of Freud attempting to solve the puzzle of how these unconscious sexual-selection-derived impulses of ours, interacting with a particular society, manifest in behaviour and personality.

For all its imperfections, Freud's theory of child development clearly informed Piaget and Vygotsky's theories (Piaget had an early, initial interest in psychoanalysis before going in his own direction, and Vygotsky was quite influenced by Piaget), and thus pretty obviously influenced the basic structure of the way that psychologists think about child development.