As a dragon god of immense power, Shenron is oddly afraid when near or in the presence of the God of Destruction, Beerus. What could be the reason?
In Dragon Ball, Shenron is the Earth's dragon god, capable of granting any wish within the limits of its creator's power. With great power, Shenron can resurrect all the dead on Earth at once or restore youth to any individual, bringing back the deceased after a year. Despite its immense power, Shenron is notably fearful of facing Beerus, the God of Destruction of Universe 7.

We've witnessed Shenron's apprehension whenever near Beerus, always trying to show the utmost respect. When summoned by Goku, Shenron immediately recoiled at the sight of Beerus. During their conversation, Shenron consistently used language that conveyed utmost respect towards Beerus. Even upon departure, Shenron attempted to bid a gracious farewell to this God of Destruction.
Many have wondered how Shenron came to know Beerus, as the Earth's dragon god seems familiar with this God of Destruction. While Shenron possesses deep knowledge of the universe's history, he doesn't know everything about it. Therefore, it can be assumed that Shenron learned of the God of Destruction through Beerus's legendary reputation.
If this assumption holds true, then Shenron surely understands Beerus's fearsome nature. As the deity of destruction, Beerus's mission is to annihilate planets to maintain balance in the universe. What's noteworthy is that Beerus acts independently of Supreme Kai orders, simply destroying whatever displeases him without hesitation.

Despite being a dragon god, Shenron possesses numerous weaknesses. From limited powers to the Dragon Balls being susceptible to turning into stone or being crushed at any moment. Additionally, if the creator of the Dragon Balls dies, they all become worthless. Furthermore, Shenron can be killed, as demonstrated when King Piccolo ended his life after fulfilling his wish.
As mentioned earlier, Shenron indeed holds tremendous power, which is why he can become a dragon god. However, Shenron's power is tied to its creator. Thus, Shenron is not as powerful as Beerus. This is also the reason behind one of the rules of the Dragon Balls, that a dragon god cannot kill a character stronger than itself or its creator. Based on this, it can be inferred that Shenron is insignificant compared to Beerus. If desired, Beerus could easily kill Shenron. Therefore, Shenron's apprehensive attitude towards Beerus is understandably clear.