A lot of reasons...(Not to use web wallets)..Below are a few which I could think of right now.
-Your coins are not stored in your actual wallet but a 3rd party wallet ,the chances of they having your private keys are 0-100.
-Since it only requires a password to hack into a web wallet,attacks of simple keyloggers or remote attacks by team viewer are more.
-Phishing Links.Another reason why you should avoid web wallets.Look around for Blockchain.info phishing links.
-No Custom access available.You cannot set your custom fees,you can't customize your transactions as you can probably do with Core/Electrum.
I agree with the last statement but with my web wallet I tend only to keep amounts below $100 & then just purchase more if I need to do a trade,
so I think in this case the risk is low especially with the longer established reputable webwallets. Also my webwallet has 2FA.