Why do we need a "routing" process in Lightning Network?
Even though Pieter Wuille has sad most of what was needed in the comments I will summarize this as an answer. 

Technically you could open a payment channel with every other person instead of creating a network with the ability to route. The drawbacks are that your total bitcoin amount has to be distributed over several channels and will be very small in each channel. Also creating channels with everyone would need way more on-chain transactions which would not directly help to reduce the load to the blockchain. 

--> Routing is needed to really reduce the amount of onchain transactions needed and to have higher liquidity per channel available.