We respect and recollect our father and mother. And in that sense, the Buddha asks us to recollect the Teacher:
AN3.70:6.2: It’s when a noble disciple recollects the Realized One:
AN3.70:6.3: ‘That Blessed One is perfected, a fully awakened Buddha, accomplished in knowledge and conduct, holy, knower of the world, supreme guide for those who wish to train, teacher of gods and humans, awakened, blessed.’
AN3.70:6.4: As they recollect the Realized One, their mind becomes clear, joy arises, and mental corruptions are given up.
And the Buddha also asks us to recollect the Dhamma:
AN3.70:7.3: It’s when a noble disciple recollects the teaching:
AN3.70:7.4: ‘The teaching is well explained by the Buddha—visible in this very life, immediately effective, inviting inspection, relevant, so that sensible people can know it for themselves.’
AN3.70:7.5: As they recollect the teaching, their mind becomes clear, joy arises, and mental corruptions are given up. It’s just like cleaning a dirty body by applying effort.
And beyond those two, the Buddha also instructs us to recall the Saṅgha, ethical conduct, and so on.
Regarding mother and father, the Buddha instructs that those who go forth first ask permission:
MN82:6.8: “Raṭṭhapāla, Buddhas don’t give the going forth to the child of parents who haven’t given their permission.”
That permission is important because those who go forth relinquish family ties. So although we respect the Buddha and the Dhamma as we should a mother and a father, we also have to be careful to pay proper attention to what the Buddha and Dhamma actually teach us.
For example, we might go to a mother or father asking for a sweet or a toy. We do not go to the Buddha and the Dhamma for sweets or toys. We go to the Buddha, the Dhamma and the Sangha for help in ending suffering. Sweets and toys do not end suffering.