This isn't true at all. Web wallets are second only to brainwallets in terms of poor security and likelihood of losing your funds. There have been countless examples of exchanges, custodial wallets, and other web services where users have lost their coins for one reason or another. You have to consider all the ways the service could lose your coins, via hacks, exit scamming, freezing your account, theft, lost keys or wallets, dishonest employees, etc., and then all the ways you could lose your coins yourself, through malware, phishing, password resets, social engineering, MITM attacks, etc. The potential vectors of attack are numerous.

If you want a secure wallet, then look in to airgapped machines, paper wallets, or hardware wallets. Even a basic software wallet like Electrum is light years ahead of a web wallet.