Bitcoin was meant to be a trustless system. You are handing over your private keys to a third party, and hence all the direct control over your funds. How do you know they are solvent? How transparent are their security measures? There are many, many examples of this going horribly wrong with people who could supposedly be trusted by the community, and there are more popping up on a regular basis.

You are asking the wrong question -- why should you trust Coinbase or anyone else?