Dumbledore distracted?

I'm doing a read-through with one of my children (we are in book 5). they asked how come Dumbledore is never around to teach Harry.

Edit: I understand that a headmaster wouldn't be teaching classes, and know what happens later in the book. This is more focused on the fact that Dumbledore seems to have at least three people's fulltime jobs.

I've thought about that sometimes. Until book 5, his titles include

-Supreme Mugwump of the International Confederation of Wizards

-Chief Warlock of the Wizengamot

-Headmaster of Hogwarts

To put that in our terms, Dumbledore is simultaneously

-Chancellor of the UK's only magic School,

-Lord Chancellor of the UK House of Lords.

Bear in mind that the 1990s House of lords was both the supreme Court and the parliament, so Lord Chancellor is head of the Judiciary, speaker of the house of lords and a cabinet member of the prime Minister at the same time.

-Secretary-General of the United Nations.

So is it completely preposterous?? or just the early whimsical world building of the books?