I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the day I become a consumer, and afterward never buy anything ever again. Rather, each and every day, my daily demand for goods is a different function than it was yesterday. Similar to the concept of marginal utility, my daily demand for goods depends in part on what goods I have already have acquired yesterday (and all the days before that in which I have been a consumer).
Let's take a concrete example. Whether I want to buy a soda today depends partly on whether or not I already have one in my possession at home that I could drink. Namely, if I purchased a soda yesterday and it's still in my fridge, I don't want to buy one today; on the other hand if I don't have a soda in my fridge, I do want to buy a soda today. My particular demand function for soda, as I just described it, depends on my present endowment of soda.
However, in the way demand is traditionally modeled, the amount of a good $x$ you wish to buy, $x(p,w)$, is a function only of prices $p$ and wealth $w$. The amount of each good you already have in your possession does not enter as a parameter in the demand function.
(Admittedly, your wealth, which enters in your demand function as a single parameter $w$, CAN be calculated from your present endowment of goods, as a linear combination of their respective market prices. But it's not the actual quantities of those endowments that enter into the demand function -- only the total money-value of all your endowments, in units of the numeraire good. That is, only the amount of the numeraire good you possess actually enters as a parameter into the demand functions for non-numeraire goods.)
I am sure that classical demand theory is not flawed. At the same time, there is a disconnect in my mind between how I think about demand (which makes sense to me only in the context of one's present endowments), versus how demand is traditionally modeled. Can someone help me bridge this gap?