Cultural and societal imagery, interpretation, and religious history is all responsible for the phrase, "sky daddy". Bear with me. The trail is loooooong.
Thousands of years ago, the concept of a dominant, kingly sky god was everywhere on the Eurasian steppe. Before airplanes, drones, and reliable climbing gear existed, the skies, and by proxy high mountains were considered the realm of the gods. The most reliable narratives we can establish about this religious and cultural understanding is in Greek mythology, but the myths and religions from Western Asia, North Africa and Europe are frequently linked through very ancient linguistic and religious traditions. So this could be said for the religious views in the Levant as well as greater Europe.
So let's use Greek mythology as an example for potential common beliefs in those ancient days. Because it's important. {Of course regional differences are expected, but the concept of a king/lightning/storm deity is well known to be shared by many cultures in this area}.
In Greek mythology, the skies were uncontested as the untouchable realm of the immortal gods. In the story of Icarus, flying too close to the heavens causes his artificial wings to disintegrate, and he falls to his death. In a more obvious affront to the gods, the hero Bellerophon arrogantly thinks himself entitled to enter their realm because of his command over the mighty Pegasus. In his story, Zeus sends a gad fly to bite Pegasus, causing him to rear and send Bellerophon tumbling down to Earth. Some say he died. Others say he lived into old age as a blind, deformed madman. Pegasus was also punished by having his freedom removed and becoming a personal envoy for the gods forever.
This is all to say the Sky = Heaven, and Zeus rules on high.
Why do I use Zeus to explain why people call the Christian God "sky daddy?" Because he's literally the reason why. In ancient Roman art, Zeus/Jupiter is depicted as a white, bearded man in a toga. Centuries later, Europe found itself in the Renaissance era, where people began to REALLY take an interest in the ancient classics again, including art, philosophy, literature, science, politics, etc. It was actually more like an obsession. Artists made TONS of paintings inspired by ancient art, but by this point, Europe wasn't pagan anymore. Images once familiar with the procession of pagan gods were reimagined with God, Jesus, Mary and the processions of saints and angels, as well as depictions of hell, purgatory, heaven, etc.
The image of a white god with a white beard dwelling among the clouds looking down is taken DIRECTLY from the imagery of Zeus and the long deep seated belief in patriarchal/sky/king figures and has become synonymous with the Christian God. And this is the image that has been popularized in modern times and is used derogatorily by people abused by the church, or by people who are angry at the hypocrisies and evils the church has committed over the centuries.
