In this world of duality, Hindu cosmology believes things happen in cycles of time. Everything must have its opposites, otherwise we will not understand the value of it. Normal human beings like us understand something, anything as a concept by comparison. Therefore day means lack of night and night means lack of day, good means that which is not bad, and bad means that which is not good. This inherent duality is in the very fabric of this manifested Universe.
Just like there is a plane of the Great Gods, similarly there is a plane of the pitris – manes – a loka whose ruler is Yama. Beyond the Great Gods is the plane of the One whose energy and power and strength is what has created this world in a way. That One is beyond time, beyond anything. But to reach that one directly for the normal human mind is impossible. It must go through progressively more advanced stages of mental evolution, pass onto the realm of the Great Gods, and THEN may enter into the realm of that One. In our physical world, the Sun is the symbol of that One, for its light pervades and creates all other lights. Conversely, every symbolism of this physical world also has corresponding spiritual significance. [Hence the necessity of rituals, for every ritual is a correspondence to another state]. During the Uttarayana, the physical sun is present in our hemisphere and thus it becomes, considering all else remaining constant, easier for a soul-spirit to pass into the higher realms after death. During Dakshinayana, the plane of the Pitris are more easily accessible. Thus it becomes easier for an average soul-spirit to pass onto the layer of Pitris after death, than the layer of Greater Gods. The Pitris are limited in their abilities, they are like us in many ways except that they do not possess a physical body.They are equally driven by desires, cravings, wants etc. They have no inherent spiritual light in them. Night symbolizes them. Dakshinayana symbolized them. Water (emotions/desires) symbolizes them. Hence we use water to perform Pitri-tarpana. Whereas fire symbolizes the Great Gods, day symbolizes the Great Gods, Uttarayan Symbolizes the Great Gods.
You may look at this from another perspective as well. The Great Gods are symbols of good qualities in us. Shiva is auspiciousness, Durga is strength, Saraswati is inspiration, Ganesha is spiritual strength/remover of obstacles, Krishna is Divine Ananda ETC. While the Pitris are those qualities in us which manifest as lust, anger, greed, unquenchable-desires, ETC. Naturally, the aim of man is to move to the higher qualities rather than these traits which make us more animal than man.
This essential spiritual knowledge was passed down to masses in the form of the idea that in Dakshinayana the Gods are sleeping. In reality, the Pitri-lokas are more awake during this time.
Of course, for a soul which has seen the inner spiritual light, it can reach the Gods in any of the ayanas easily. But for maintaining world-dharma, it is important to understand the essential difference between these two ayanas and their energies. During Uttarayana we worship the Mother Goddess in per peaceful and spiritually uplifting form, also known as Basanti Puja. During Dakshinayana we worship Her as Durga, the slayer of demons and asuras, which manifest in us a negative qualities, and in the world around in negative ideas, people, forces ETC.
And that is why in the Mahabharata, Bhisma waited till start of Uttarayana to leave his body. This is the crux of it all!