What critical issue in symmetric and asymmetric encryption is resolved by using a hybrid method like diffie-hellman?

Key exchange. If sending and receiving party did not agree on keys in an out-of-band way, the keys will have to be sent via the same channel as the encrypted data. Diffie-Hellman is an algorithm to let both sides derive the same key without physically sending it over the channel. An eavesdropper can listen in on the channel and still is unable to get the key.