What is Core's excuse to avoid increasing bitcoin block size to 2mb?
Just imagine when the miners a mining a small rock then they suddently have to mine a really big rock, they will we stuck there for a long time that cause the chain stop.
NO, NOT TRUE. The mining speed will not be affected by the block size, at least not significantly. The merkle root is indeed, hashed by the miner to place it into the block header. However, it is not hashed repeatedly, it is only hashed once before it is passed to the miners in a pool. The tradeoff for this is worth it.
However, the propagation time for bigger blocks can potentially be longer and this can cause blocks to get orphaned. It would take more time for nodes to process it too. Miners are generally not very affected*.
*Well SPV mining.