Brahman is the father/mother of Lord Shiva because he is his manifested form. Lord Shiva is Swayambhu and was there before the time and will be there forever. But there are different stories in different Puranas that claim otherwise.

Is Brahma the Father of Lord Shiva?

There are some stories in the Puranas, which imply that Lord Brahma is the father of Lord Shiva because he created him, but these stories are not widely accepted.

According to the Vishnu Purana  (Book I – Chapter 8), at the beginning of the Kalpa, as Brahma purposed to create a son who should be like himself, a youth of a purple complexion appeared, crying with a low cry, and running about Brahma. When he beheld him thus afflicted, said to him, “Why do you weep?”

“Give me a name,” replied the boy.

“Rudra be your name,” rejoined the great father of all creatures: “be composed; desist from tears.” But, thus addressed, the boy still wept seven times, and Brahma, therefore, gave to him seven other denominations; and to these eight persons regions and wives and posterity belong. Then, the eight manifestations are named Rudra, Bhava, Sharabha, Ishana, Pashupati, Bhima, Ugra, and Mahadeva, which were given to them by their great progenitor. He also assigned to them their respective stations, the sun, water, earth, air, fire, ether, the ministrant Brahman, and the moon; for these are their several forms.

There is another story which implies the same. Lord Vishnu was the only one who survived Maha-Pralaya. After some time, he started recreating the universe by giving birth to Brahma. Lord Brahma was born out of his navel. Then he created Lord Shiva from his forehead. That is why Lord Shiva is always meditating.

“The four-faced Brahma emerged out of the navel of Mahavishnu who was reclining on the serpent bed in the ocean. Lord Siva appeared from the forehead of Brahma.”

– VP Krishna Janma khanda 41.70

Is Maha-Vishnu the father of Lord Shiva?

According to Brahma-Samhita, Lord Shiva was born from the space between the two eyebrows of Maha-Vishnu.

“The same Mahā-Viṣṇu created Viṣṇu from His left limb, Brahmā, the first progenitor of beings, from His right limb and, from the space between His two eyebrows, Śambhu, the divine masculine manifested halo” – Shri Brahma-Samhita 5.15.

The Birth of Lord Shiva:

The story of Lingodbhava narrates the appearance of Lord Shiva. Per the Shiva Purana, once when Lord Vishnu and Lord Brahma were arguing about who was superior, a huge infinite pillar of light appeared between them.

They forgot their fight and decided to test it. Lord Brahma assumed a form of a swan and went upwards. Lord Vishnu took a form of a wild boar and went downward. They both traveled for 1000 years but could not find the end of the lingam. Therefore, they returned to where they started.

They bowed to the lingam and wondered what it was. Then a loud sound “Om” came out of the column, and the letters “अ” “ऊ,” and “म” (“a,” “u,” and “m”) appeared on the lingam. Above those letters, they saw Lord Shiva along with the goddess Uma. Lord Shiva told them that they both were born out of him, but they had forgotten about that.

Thus, Shiva Purana states that Lord Shiva is the father of Lord Vishnu and Lord Brahma, which conflicts the other Puranas.

“I am My Great-Grandfather”:

Once a sage asked a question to Lord Shiva:

“O Lord, who is your father?”

Lord Shiva replied, “Brahma is my father.”

The sage asked, “So, who is your grandfather?”

Lord Shiva replied, “Vishnu is my grandfather.

The sage again asked, “Who is your great-grandfather?”

Lord Shiva replied, “I am my great-grandfather.”

This story is confusing and does not directly answer the question “Who is the father of Lord Shiva?” It is possible that Lord Shiva said so because Rudra is his incarnation and Rudra was born to Lord Brahma and Lord Brahma was born from the navel of Lord Vishnu. But Lord Vishnu was born from Lord Shiva.

Conclusion:

Because of the conflicting stories in the Puranas, it is hard to answer the question with confidence but in general, it is believed that Lord Shiva and Lord Vishnu are self-manifested and hence have no father or mother. But Lord Brahma was born from the the lotus originating from the navel of Lord Vishnu.