Why is replication on one strand of dna continuous, while on the other strand the replication must be discontinuous?

This is because DNA polymerase can only add new nucleotides in the 5’ to 3’ direction. In the replication bubble, the continuous strand is 5’-3’, however the discontinuous strand is 3’-5’. This forces DNA polymerase to use small primers and work backwards on the discontinuous strands, forming Okazaki fragments.