Why is it important that miners mine at the end of the longest branch? 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?
Lets imagine that a fork is created during the propagation of a block in a certain height h. Two valid blocks are created and spread along the Bitcoin network. The majority of the miners start mining on block hA, while the miner m you mentioned (or actually a mining pool since a single user with such mining power is quite unlikely to exist) starts mining on the top of block hB.

The odds of mining a block on the top of hb before the rest of the network mines on the top of hA are lower that the other way around, but since the mining power m and the rest of the network are not that far from each other, it can happen (actually, it will happen, sooner or later).

Moreover, the hashing power of the network is split, and a huge part of it is wasted (either m's or the rest of the network), so the elapsed time between blocks will grow, until a recalculation of the difficulty is performed (some point between 1-2015, since it is recalculated each 2016 blocks).

Other papers has talked about similar things in the past (selfish mining techniques) concluding that with even less mining power similar attacks can be achieved.

By using selfish mining techniques a malicious pool can benefit from mining in a "secret branch" and reveal blocks just when they are ahead of the public branch by 2+ blocks, earning all the mining reward and making other miners waste their time, or when a block is propagated by other sources, trying to get their block picked up by a majority instead of the other.