Why does the Pokémon count show one more than the actual Pokémon I have?

I have 11 Pokémon, none duplicate. But the count at the top shows 12.

Is this a bug, or does it count the Pokémon in the egg, too?

Solution 1:

'Total Pokémon' is a count of all currently held pokémon and eggs

In the example you give, you are currently holding 11 pokémon, and 1 egg. The given pokémon count is 12.

This is likely in order to prevent bugs related to issues that would otherwise arise when you have a full box of 250 pokémon, and could proceed to hatch more, through eggs.

It is worth addressing that this is a total held pokémon count, not a count of unique pokémon. If you did have duplicates in your box, they would also contribute to your final count.