The reason coffee is not ho’eitz is because all the coffee that was put in the water is then taken out. It’s like a vegetable soup from which all the vegetables were removed after cooking.
While our modern science of physics tells us that since the soup is not pure water there must obviously be some substance of the vegetable left, and that if we were to dry out the vegetables we removed and then weigh them we would inevitably find that they weigh less than they did when they were put in, the halacha’s view is different.
The halacha’s view is that color, taste, and smell have no substance themselves, no mass, but are merely properties that a substance has; מראה אין בו ממש, טעם אין בו ממש, ריח אין בו ממש. When you cook vegetables in a soup and then remove them, the same vegetables went in and came out and all that they did while they were in the water was to impart to it color, taste, and smell. What you have left, according to halacha, is not water with particles of vegetable in it, which carry color, taste, and smell, but rather pure water that happens to look, taste, and smell differently from normal water, because it spent time closely associated with the vegetables and learned to copy them.
Therefore the bracha on the soup — or on the coffee — is the same shehakol that we say on normal water. If we were to drink the coffee itself together with the water, then the bracha would be ha’etz. Which leads us to the question of hot chocolate, and the achronim struggle to understand why we should not say ha’etz on it, since the cocoa powder is not removed but is drunk together with the water. (The achronim do not discuss chocolate itself, i.e. the hard substance that we call chocolate stam, because it was not invented until about 1800. All mentions of “chocolate” in achronim refer to hot chocolate.)
This leads to the question of instant coffee. “Reb” Eliezer, with his “daas baalei batim”, thinks it’s more obvious to say shehakol on instant coffee than on regular brewed coffee. But the opposite is true. What is instant coffee, after all, but brewed coffee from which the water has been removed? If it were indeed true that color, taste, and smell have no substance, then instant coffee could not exist. The jar would be empty. But the fact is that when we buy the jar it is full, and we take a spoon of this very real physical substance and dissolve it in water, and drink it without removing anything. So it’s harder to understand why it’s not ha’eitz.
By the way, this same principle that color, taste, and smell have no substance, is why if you spill wine into a mikveh and the water’s color changes it is pasul, but if you soak a dyeing substance in fewer than 3 login of water and remove it, and then spill the water into a mikveh and change its color, it remains kosher. The halacha regards the color that the dye imparted to the water as having no substance, while the wine obviously does have substance.