A few points worth covering. The most important and common reason for sticking has been mentioned, but it's worth recognizing its importance. Browning meat will release when it's ready. Sticking occurs when you try to rush it.
Stainless steel pans do need careful handling. Stainless steel is soft and gets softer when hot. It is easily scratched. Scracthed increase the chance of sticking when everything else isn't exactly right. Oil has to fill in all the other than flat spots, and excess scratches is asking for trouble. I do not use metal tools or abrasive cleaners on my stainless steel. Nor do I allow them to go into the dishwasher. That's a very harsh environment. Nor do I allow any deposits to accumulate. But stainless steel that has been damaged by long abuse with metal and abrasives can no longer be considered "non-stick" and should be discarded if they're your only cookware.
There is always much discussion about the virtues of hot-pan-cool-oil or hot-pan-hot-oil. But from a stainless steel sticking perspective food should go into a hot pan with hot oil. Hot oil better fills the fine faults in the metal surface. And there are always flaws, even in new pans.
Do not get too fixated on the high heat notion. High heat is appropriate for browning meat, but a lot of other cooking calls for low to medium heat. This is a difficult topic to talk about without live demonstration. When you need high heat, you really need high heat. But we can't put a label on the proper heat setting. There is far too much variation among ranges and between gas and electric.
Sticking is not all bad. You should never have to pry meat off the pan surface, leaving meat behind. But you also don't need and shouldn't expect to always have all food lift off without a trace. Without some material sticking to the pan, we would have rather poor gravies and sauces. But the caramelized material that's stuck should come off cleanly when deglazing with wine or other liquid. And if you think about it, for these desirable products of deglazing you require sticking. You just require it to release, too.
Eggs are a terror for many cooks. There's a finely defined point where enough oil and enough heat cooks eggs rapidly without sticking. I don't spend a lot of time hunting for it. I have one and only one pan with a Teflon type coating, a small fry pan for omelets. To learn to handle eggs in stainless steel, start with fried eggs and work out the correct situation, flipping when the whites start to set. Oh, and as with all foods, use room temperature eggs.
And stay away from cooking sprays. They will tend to gum up the pan surface, which will cause sticking. Heavy bottom pans will tend to stick less, because they will heat more evenly across the surface, and they will tend to stay flatter.
