Two sentences. One says the dog did the biting, the other says the man did. Watch what survives when you drop the words into a bag and keep only the counts.
The dog bites the man
The man bites the dog
The bags are still filling.
The words arrive in a shuffled order, because the bag does not care when they arrived.
Once both sentences are in, the two bags hold exactly the same five counts:
the 2, dog 1, bites 1, man 1. Nothing in the representation can tell you
who bit whom.
That is the trade. You get a fixed-length vector you can compare, cluster and feed to a classifier, and you pay for it with word order. Every model in the rest of the course is, in some sense, an attempt to buy that order back: n-grams keep a short window of it, recurrent networks carry it forward, attention learns which of it mattered.