[ornitorrincos]

It does have two international airports:

https://en.wikipedia.org/wiki/Berlin_Tegel_Airport

https://en.wikipedia.org/wiki/Berlin_Sch%C3%B6nefeld_Airport

Although they are planned to be closed when the third one opens(this one doesn't have a lack of issues though):

https://en.wikipedia.org/wiki/Berlin_Brandenburg_Airport

[hknd]

I think people think at something like FRA or LHR when talking about an international airport.

Tegel+Schoenefeld have combined ~30M passengers per year. FRA has ~65M, and LHR has ~80M.

Number of intercontinental flights from Berlin is just super low s.t. most business travelers fly do a stopover in FRA.