Like alot of companies, they made decisions that made sense at the time that ended up having poor long term consequences.
When they decided to really grow it was due to a couple of things..
1) Their competitors were all doing the same thing and they almost needed to grow their investment arm and international presence just to stay in business.
It used to be that Audi, Porchse etc would come to them for basic loans etc and business was good. But as these firms grew internationally they also needed a bank that did the same.
Audi sells in Brazil it needs a bank with a presence there as well. And along comes the big american and European banks who start selling themselves to Deutsche's current clients as a one stop shop who can do what Deutsche does but also all these new things that international modern companies need.
A company needs to get a currency or interest rate swap, well Goldman Sachs can do that, so Deutsche followed suit.
From this perspective its easy to see how they started down the road they did.
And once you start building out a international team of investment bankers and traders that means you're now competing for talent with the rest of the big players.
So how do you hire the best traders/investment bankers?
You pay them like everyone else does, which is to say you have to pay them..... alot.
You have to provide perks like New York/London/Tokyo offices and the ability to trade the hottest products and markets.
You need to let your traders make money like other firms do or they'll just leave for those other firms.
All just to keep your existing clients.
And before long you are just like everyone else.
Then in the mid 2000's during a huge bull market you have one of wall streets stars Boaz Weinstien (https://en.wikipedia.org/wiki/Boaz_Weinstein or read "The Quants") running your derivatives desk. And they made money hand over fist..... at the time.
Now the funny thing about bull markets, is that even bad trades can make money during them because everything is up and to the right.
And even if you think you are putting on too much exposure, tough, remember that so is everyone else and if you stop, then the good traders and bankers quit and go to competitors who will let them make money.
It's sort of like raising money as a startup in frothy markets. You'd just better raise money because if you don't and all your competitors raise 20 million then even if you're better they'll often win because they can survive longer than you.
It just happens that Deutsche didn't quite understand the game that was eing played, and when the music stopped, they were holding the bag so to speak.