Why do calligraphers call themselves "my dear friends" compared with their younger counterparts?

This is a compliment.

Dear friends refer to people who are older than themselves among friends of the same age.

Calligraphers' signatures should be commensurate with their peers, modest to themselves and respectful to others. Calligraphy communication is the embodiment of personal accomplishment, without overemphasizing age, seniority and qualifications. Calling yourself humble and respecting the donee not only reflects good cultivation, but also asks for advice from the other side.

When I was in college, the vice principal of the school wrote me a word, calling me "Xiong Xue" when I signed it, which was commensurate with my classmates and a modest name.