The line between decentralised and centralised wallets is blurred. Electrum lets you keep your private key but connects to the Bitcoin network through one of a limited number of servers. Blockchain.info lets you keep your private key but you must access the Bitcoin network through its website. Coinbase is fully centralised because you don't know your private key, but Electrum and Blockchain.info are partly centralised.
How is electrum centralised when your private keys never leave your pc and you can do what ever you like with your coins. The only thing electrum needs is an internet connection. Centralized mean some central supreme authority watching over you and making decisions for you, decentralized mean no central authority, you are free to do what you like, thats the big difference between Electrum and Coinbase which don't let you know your private keys.
Electrum's wallet connects to the Bitcoin network through one of a number of servers. One of those servers is what relays all your transactions to the Bitcoin network.
You have to trust the server isn't malicious. If it's malicious your Bitcoins are less secure. This is not entirely true as all that a malicious electrum server can really do is prevent you from spending your coins (via electrum), spy on you and tell you that you have a 0/unconfirmed transaction that has not been sent to the rest of the network.
With the full Bitcoin core wallet it doesn't matter if your wallet connects to a malicious node because it connects to multiple nodes at the same time, and ignores any malicious one.
Also not entirely true as if a malicious entity is able to connect to your node multiple times then your node might not be able to detect that they are connected to a malicious node and would not know to ignore it.
This answer does not apply to me personally, however I do think it applies to many Bitcoin users, as well as an even higher percentage of potential Bitcoin users - I think that many people do not possess the technical abilities to keep their private keys both secure and properly backed up and I envision that many people will use online wallets like coinbase (how it is setup currently) to protect their money and facilitate the spending of their money. There has been a lot of money both lost and stolen by/from people who were the victims of bitcoin stealing malware, hacking, and poor backups.