Do you trust yourself to manage your own private keys?
Yes, of course. Why wouldn't I?
Criticism often comes to online wallet providers (Xapo, Coinbase, etc) saying, if you don't own your private keys, you don't actually own your bitcoin. On the other hand, if your cash is in a traditional bank, you don't really own your cash either.
They are both true. I don't trust any online service to keep my funds. I don't trust banks. You know governments have ability to freeze your bank account, and take all of your money.
I think about pictures, movies, files, documents, I had on my computer 10 years ago (and I always backed up), and I probably couldn't retrieve a single one without relying on a cloud-based service (Facebook, Google Drive, Dropbox, etc.). I have no idea where the original photos of my trip to Indonesia in 2008 are, but I know that album is still easily accessible on Facebook.
Cloud services, are you serious? Privacy = 0
I never use cloud services. Do you like it if some random people view your photos just because they want and can?
I rarely upload a photo of me on the internet. I don't want to keep any of my files in cloud services or random sites.
Are critics right to say, don't use an online wallet provider, it's not safe?
They are not safe enough to keep all your funds, but they are useful if you will use small amounts or use them in short time.