The stock is an asset that has value. This view makes a lot more sense when the stock is liquid and you can go and get rid of it right after you exercise your option.
I agree that this totally sucks if there is no easy/public market for the stock.
The option was an asset that had value as well. We do not generally charge capital gains on assets with values until they actually get turned into money. If a stock that you bought traditionally appreciates, or your house does, you don't pay cap gains on it unless you sell the asset in question.
I appreciate that in this case you're turning an asset into a slightly different asset, and that's not like just ordinary appreciation, but I don't know why it really matters. A rule of "capital gains gets charged when you turn an asset into cash" makes sense.
I agree that this totally sucks if there is no easy/public market for the stock.