To begin, anyone who says "RPG means Role-Playing Game, and you play the role of Link, so Zelda is a RPG." is stupid. You play the 'role' of the paddle in Pong too. If you disagree, please Click Here. Besides, 'RPG' doesn't even mean 'Role-Playing Game' anymore, it means 'RPG'. A 'Role-Playing Game' applies to games that hearken back to pen & paper games such as those found on PCs, wheras RPG applies to games like Final Fantasy and is almost always on consoles.
Let us start by defining what a genre is. A genre is a group of similar categorized items. Genre's are usefull because thay allow one to give another a general idea of what something is like quickly> When describing a sitcom to someone, you don't say "It's a half-hour show that has an ensemble cast that gets into a new funny situation every episode with the hopes of making the audience laugh." That's stupid, you say "It's a sitcom." And in saying that, the person has a good idea of what that show is like.
So is it more useful for a genre to pretty specific, or very broad? Consider 100 objects, with 10 groups of 10 objects of a different shape (10 circles, 10 trinagles, etc.). 5 of these groups are are all red, the other 5 groups all blue. You want to tell someone about one of the objects, when they know how the system works. Will they get the better idea of your shape if you say it is red, or that it's a triangle. 'Red' could be any of 5 different shapes, whereas the triangles are all similar, and they already know that all triangles are red. Of course it's better to say your object is a triangle, it gives a FAR clearer idea of what the shape is.
How does this figure into the great Zelda-RPG debate? Sure, Zelda has a lot of things in common with traditional RPGs, dungeons, items, etc., but the meat of the gameplay is so inheritly different, that they just aren't the same thing. They may all be red, but they're different shapes. I could say that Zelda, Final Fantasy, and Secret of Mana are all similar, but they are only so in the general sense. A difference between 'genre' in the general sense and 'genre' in the specific sense as far a games are concerned centers around fundamental gameplay. If the fundamental gameplay of a group of games are very similar, they would be of the same specific genre. A broad genre applies to games similar in spirit, scope, and pacing, but different in regards to fundamental. Dungeons, items, and money would be examples of 'spirit, scope, and pacing'; wheras experiance points, turn-based or menu-based battles, and an 'overworld' would be fundamental parts of gameplay. They have a very large say in how a game is played.
The tricky part comes in naming these genres. The popular terms and a definative example of each would go; RPG (Final Fantasy), Action-RPG (Secret of Mana), and Adventure (Zelda). But what to call this collective group (the 'broad' genre)? One could at this point say that the collective is 'RPG', but that is just too confusing. Zelda is a Rpg/Adventure, while Final Fantasy is a RPG/RPG? No. Personally, I like to call this broad group "Epics". Actually, I see all games as falling into 2 broad groups, "Action" and "Epic". Action games being based on seeing and doing, epics being based on thinking and doing. Of course there will be games that split between these; Metroid has a lot of action-based gameplay, but is ultimatly based on exploration. Many more fall squarely between, namely platformers and survival-horror, both of which feature much in the way of puzzle solving, but are slightly too fast-paced. But I digress. Ultimatly, to call Zelda an RPG under the general sense would mean that real RPGs would have to be called something different.
Now, specific examples from the games highlighting the differences between two epitomes of their respective genres, Final Fantasy VI and A Link to the Past;
Look at the battle systems. One is turn and menu-based, the other is action-based. They play completly differently. Now I don't know about you, but to me that looks like a major difference in each title's fundamental gameplay.
What about items? Items are used differently in a RPG and an Adventure. In an adventure game, items grant you new powers and allow you into new areas. In a RPG, items are mostly used either to strengthen your character (armor, weapons) or as some sort of enchancment item (potions, etc), but for the most part are in no way required to complete the game (though it's effectivly impossible).
Status and experiance. Here is another big difference. Notice the experiance points in Final Fantasy? See the way heart containers are gained in the Zelda screen? That heart-container is about the closest to an experiance system that you'll see in a Zelda game, which to me is hardly similar. Also, look at the use of status values (strength, agility, etc) in Final Fantasy. They dictate damage given, taken; most of what occurs in the battle system, and the way in which these values are used vary somewhat randomly, the same attack by the same enemy on the same character can yield very different amounts of damage. The damages given and taken in Zelda and other Adventures is set and changes only when equipment is upgraded.
Now, why isn't Zelda considered an Action-RPG? When looking at a definitive Action-RPG like Secret of Mana, one sees that an Action-RPG is effectivly exactly like a RPG, except that the battles take place in real time. This is still very different from an Adventure like Zelda. Attacks are still based off of status values and may yield different values for the same actions, items are still mostly used in equipment and for healing/enhancement, and there is still an experiance system. Ironically, Zelda II: The Adventures of Link is almost a text-book example of an Action-RPG; experiance, attack values, a definitive overworld, etc.
So, why is Zelda still considered by many to be a RPG? Just because a game defines its own genre doesn't mean that it must be a part of some other genre. And no one would want the series to become more like traditional RPGs, so why is there even a debate?