Coolant hoses are very much like the blood vessels of a car. If a heater hose or radiator hose fails you only have a few minutes to stop the engine, after which it's often too late. Hoses fatigue and wear out, of course, but another mode of failure is improper installation or removal. Unfortunately, when failure occurs in the latter case it's usually an associated (often expensive) component to which the hose is attached.
Two common installation mistakes are: 1 - choosing the wrong size hose, and 2 - clamping it too tight. Another common mistake occurs when someone wrestles the hose onto its connection with too much force, thereby cracking or breaking the connection. This happens most often while installing heater hose on the [relatively] delicate core, and sometimes while removing hoses from copper radiators.
That brings us to the removal process and RULE # 1:
Never pull or twist a hose off a connection if it has been installed longer than a few minutes! Always cut the hose off!
Hoses that have spent any time on the car become "cemented" to whatever they are clamped. They don't readily slip off, so uninitiated persons tend to try to twist them to break the seal between the hose and the metal. Damage (requiring replacement) occurs as often as not, so don't let your radiator or heater core be added to the scrap heap before it needs to go there.
Use a utility knife or razor blade to cut the hose linearly where it is connected. Cut through until you feel metal on the inside and then gently pry up the edges and peel the hose end off. Once the hose is removed take the time to clean the surface of the metal before installing the new hose. Use fine sandpaper, steel wool, etc.
You can just as easily break a radiator or heater core bib (that's what the connection is called) by twisting a new hose on, so STOP! Go get some Armor All or liquid dish detergent (don't use oil or grease!) to use as a lubricant. Spread some on the inside of the hose and then push it onto the bib. You won't believe how much easier it is when you lubricate the hose.
Don't forget also to slip the clamps over the hose before installation. It's much easier to do it beforehand than trying to snake a clamp end around later.
This brings us to Rule #2:
Don't over-tighten the clamp! Tighten the clamp just until the hose bulges slightly in the area next to the clamp's metal banding.
Tightening a clamp too much causes the rubber to split and break down internally. This leads to premature failure of the inner cords and then shock and vibration will take it toll on the hose, leading to total failure.