Generally, what we call jetpacks are technically rocket packs, because they work the way rocket engines do: by combing fuel, usually hydrogen, with an oxidizing agent. The chemical reaction produced by the fuel and oxidizer is highly exothermic, meaning it releases copious heat energy. The resulting hot gas shoots downward to provide thrust.
1. Humans are not designed to fly!!!!!!!!!!!!!!!!!!!!!!
2. Thrust burns a lot of fuel!!!!!!!!!!!!
3. Danger!!!!!!!!!!!!!!
4. Rockets and jets are really, really loud!!!!!!!!!!!!!!!!!
5. Inefficiency!!!!!!!!!!!!!
6. Pollution!!!!!!!!!!!!!!!!!!!!