I am reading about Tirpitz and I see that he was one of the chief individuals in the Imperial German leadership responsible for advocating that Germany attempt to directly challenge British naval superiority. If I understand the conditions of that time correctly it was completely irrational to expect this could be achieved successfully because the British a) would simply not tolerate another country having a more powerful navy and b) enjoyed the luxury of being able to skimp on their army enough to achieve any plausible limit of necessary spending. What exactly did Tirpitz and the other Germans see that made them think differently? The situation reminds me of the Command and Conquer Red Alert 2 intro ("we'll retaliate, you know") except the Germans didn't have a magic Lenin lookalike to prevent the British from building a lot more battleships in response. The factors I can think of are overinflated sense of national capabilities, misreading the diplomatic situation, and simple wishful thinking, but I'm not sure in what proportion or if I'm missing any others.
Tirpitz's phrase was it was a 'risikoflotte' - a 'risk fleet' or less literally a deterrent rather than a full-on contest. What was it meant to deter? From the design (short-range, heavily-armoured line-of-battle ships optimised for conflict in the North Sea and adjacent waters) it was meant to threaten British control of its home waters - and hence its connections with the Continent and the Empire. So leaving Germany a freer hand with regard to its Continental rivals.
The British navy had world-wide commitments. The German navy - apart from a small number of cruisers and commerce-raiders - could concentrate all its capital ships in the North Sea. In theory, it did not need to match total British numbers.
In practice, the British responded by getting closer to the French, so freeing up resources from the Mediterranean (the second-largest commitment) then, when the Germans refused naval arms limitation, building two for one. Also, HMS Dreadnought made the first decade of German investment obsolete at a stroke, while being part of broader changes that freed up British resources to concentrate on the German challenge.
So inflating their own capabilities, misreading the diplomatic situation, wishful thinking. Very typical of Wilhelmine policy. There was also domestic angles - for one the ships were part of the 'marriage of iron and rye' - the political alliance between Ruhr industrialists (who benefited from the ship-building) and the Prussian junkers (who got food tariffs in return); a second angle was that an impressive navy appealed to centrist nationalist middle-class opinion - a key group in fending off Social Democratic advances in the Reichstag (Tirpitz launched the Navy League to build support here); a third angle was to lure north German industrial workers away from the SDP with both jobs and patriotic appeal (this failed - they remained resolute Social Democrats).