The tank gun has its origin in the 88mm anti-aircraft gun. Anti-aircraft guns need high velocity to get shells up to where the aircraft are. The larger the shell they can get up there, the better. However, its also better to get more shells up there, and the larger the shell, the slower they are to handle and load. In particular, it's an advantage to have fixed ammunition, with shell and propellant together, like giant rifle ammunition. It's common for large guns to have separate shell and propellant - this makes them easier to handle, because the individual parts are lighter than fixed ammunition, but slower to load. The bigger the calibre, the heavier the ammunition, and at some point, fixed ammunition becomes to heavy to be easily handled. This limit tells you the biggest calibre you should use for a manually-loaded quick-firing anti-aircraft gun.

A number of different calibres were chosen by various countries for this biggest fixed-ammunition manually-loaded gun, from 85mm to 94mm (Soviet Union: 85mm, USA: 90mm, Germany: 88mm, Italy: 90mm, UK: 94mm (3.7")). The German choice was based on earlier use of the calibre in the navy, where the choice was made on the same basis: weight of the ammunition. The anti-aircraft and anti-tank 88mm guns were different designs, not based on the naval guns. The advantage of choosing the same calibre was that existing machinery for making barrels and shells could be used. The naval guns have an old history, used, e.g., on Oldenburg, laid down in 1883, and the following Siegfried class, the first of which was laid down in 1888. This was before the aeroplane, and thus they were not anti-aircraft guns. They were intended for use against torpedo boats (for which quick-firing is desirable); since the guns were relatively light, they were also used by torpedo boats.

(88mm isn't strange if you're British - it's just a metrified 3.5". The equivalent UK anti-aircraft gun was 3.7" (94mm), and can better be accused of being an "odd" caliber.)