In this paper, the authors present a simplified description of mining strategies. The strategy which they call "honest strategy" is to always mine a block at the end of the currently longest branch. They claim that, if a miner has a very large computing power (above ~45% of the total power in the network), he might gain a higher profit by deviating from this strategy and using a "dishonest strategy" - mining at a shorter branch - hoping that at some point his branch will become longest and be accepted by the community.
They claim that this "dishonest strategy" is problematic, but I do not understand why; what can happen to the bitcoin network if some miner will use this "dishonest strategy"? As far as I understand, he will not be able to create a "double spending", since such a double spending can be easily detected by any other node reading his branch. So what else can happen?