As far as I've understood an attacker can destroy the Bitcoin-network if he solves several blocks in a row.
You've understood incorrectly. All an attacker can do is reverse some of their own transactions, or delay other transactions from being confirmed. This will not "destroy the Bitcoin-network". Blocks are orphaned on a daily basis, this does not result in destruction of the Bitcoin network.
Say the attacker needs to solve six blocks in a row to destroy the network.
Why not say that the attacker needs 100 blocks to destroy the network (since they can't even spend any of their newly mined bitcoins until they have 100 confirmations).
What I wonder is
1) Is my premise wrong?
Yes. Your premise is wrong.
Can bitcoin be destroyed if one attacker mines several blocks in a row?
That depends on what they do with those blocks, and how many they mine.
2) Is there something else that makes 51% the threshold for being able to destroy the network?
If an attacker can maintain more than 50% of the total hasing power of the entire network, then they are guaranteed the ability to mine EVERY block. This means they can prevent ANY transactions from EVER confirming. It means they are guaranteed the ability to arbitrarily roll back thousands of blocks. It means they are guaranteed the ability to reverse EVERY transaction they send.