It won't fit in your back pocket — If you're the type to stick your phone in the back of your jeans, don't get a phablet. It'll be either too tall or too wide to fit properly, making the device more susceptible to theft.
Awful for people who ride public transit — You never know when you won't score a seat and you'll need to hang on for dear life in one hand and use your phone in the other. Most phablets require two hands, so don't make your life even harder, bus surfer, by getting a bigger phone.
Not ideal for making actual phone calls — With a wider, taller screen, you're more likely to get face grime all over your giant phone. It's awkward to put up to your ear without pressing it to your entire face. Get ready to invest in a Bluetooth headset if you want to take phone calls on your phablet.
It's heavier — Stating the obvious here: a phone with a bigger display isn't going to be as lightweight as a smaller phone, even if it is thinner, like the iPhone 6. It'll mean an extra ounce in your already heavy bag or backpack.