Wikipedia makes whipped cream look very simple: gas bubbles are trapped in the fat and create a colloid. However, we all know that you can easily come across "whipping cream" that just won't whip even with all the necessary precautions. Meanwhile a different cream will whip up in a matter of seconds even at room temperature. This is despite both having the same fat content and ingredients.
Furthermore, in my experience, if you take a product with the same or higher fat-content but with animal of vegetable fat instead of butterfat, then the consistency of Chantilly cream will be impossible to achieve. (With, perhaps, the notable exception of coconut cream although I can't say it worked well for me.)
Why does this happen? What is the physics/chemistry behind this discrepancy? Obviously, something sets real whipping cream aside. Something other than just fat content which allows the colloid to appear.
NB. I know, the Internet is full of lists of "whipping cream substitutes" ranging from nut butter to pureed onions. I'm pretty sure, however, that most of these will not incorporate air and fluff up anywhere near as well as homogenized heavy cream.
Best Answer
Cream itself is a colloid made up of butterfat & water. That colloid is uniquely suited to have the air incorporated to create whipped cream.
The chemistry of whipping cream is more complex than just "fat + air = whipped cream". If you're trying to whip olive oil or lard into "whipped cream" then each fat will have some unique additional steps to make it hold the structure.
For example, adding a dash of acid and an egg yolk (which contains lecithin, an emulsifier) to olive oil will help create a colloid when whipped. In this case, the resultant colloid isn't whipped cream though--it's mayonnaise.