Common faucet fittings (e.g. by Delta, Danze, and others), are a snap to install, but cannot be removed by releasing the four tabs. Use the following technique to properly disconnect the quick connect fittings.
1) Press up firmly on the hose
2) Press down on the top piece
3) Pull the hose down
Type 1, 2, and 3 fittings are documented further here:
http://www.premierfaucet.com/faqs/faq-06-how-to-disconnect-a-snap-connect/