I don't understand why the finesse has to be personal in this case.

Hello Nora, in this context you can take 'finesse' to mean that Markus had an impressive level of social skill. Another way of saying it would be that he handled the situation confidently and skilfully, perhaps even with style. See meaning number 2 in this dictionary extract: <https://www.merriam-webster.com/dictionary/finesse>;. Hope this helps!

Finesse is to be delicate and precise, careful and specific. Personal finesse implies Chen was good at learning English carefully to pronounce each word correctly.