why mercury electrodes are not used in dihydrogen preparation?

You may have only read from books and learnt about Standard Hydrogen Electrode (SHE). If you had used it in your experiments, you would immediately realize that it i it is so cumbersome to handle it. Then you would think how nice it would be if there was a simpler and more convenient reference electrode and your search would lead you to reference electrodes such as calomel electrode, Ag/AgCl electrode etc.

In fact this is how they were discovered - in a search for a simple, reliable and easy to handle reference electrode.

Therefore, the answer is: easy reliable and simple to handle make calomel electrode, Ag/AgCl electrodes more commonly used compared to SHE.