I actually don't think they got arrogant
I think they got scared.
The iPad and the sudden rise of tablets scared the bejeezus out of MS. They had faffed about for so long with their own touchscreen system and wen't down so many blind alleys (I tried out MS touchscreen desktop prototypes at a Birmingham NEC hosted tech show 20+ years ago) that they thought they had no good answer to the rise of Apple and Android.
Everything they have done in the personal computing space since then has been a reaction to that fear. The purchase of Nokia Telephony, the rushed and incomplete W8 (and subsequent release of W10), the Surface have all been about trying to keep control of the personal computing market, and forgetting that their core revenue was actually the corporate computing market.
W10 still isn't a corporate ready O.S.