I'm A Banana
Potassium-Rich
Here's why I don't think it was a bad reason to give: The logical reason starts arguments.
Well, arguments come from unsatisfied players, IMXP. Very few people enter a game going "You know what would be a lot of fun? Debate about rules minutae in a make-believe game about elves and magic." If they're arguing, it's generally (though not always) because their fun is being shut down.
Looking beyond the argument in your examples, you can see that the player was frustrated because they had what they thought was a cool idea, and the DM basically said, "No." So the player defended their idea. Not the right thing to do (DM's say always goes), but understandable because they would have more fun having their idea work than having it shut down. The only difference in the second example is that the game itself is shutting their idea down based on a technicality, rather than the DM shutting their idea down based on the DM's judgement. A player that respected or understood the DM's reasoning would react the same way in the second example, and a player frustrated with the game's reasoning will decide that the game itself sucks and argue against the game's rules rather than the DM's rules.
And that boils it down to the essential problem: it is fun to use elements of your character in new and innovative ways. It's the basic "fun of using tools" that people have. The same rush that the caveman who came up with the idea of sharpening a stick had when he stuck it into an animal. "My imagination and cleverness have expanded my abilities!"
It is fun to use fireballs to melt door ice, even if they are mostly made for damage or combat.
Which explains something of the resentment in some folks the game's tendency to say "rules are results, insert whatever flavor you want." It shuts down creative uses. This is good for game balance and DM control, but can certainly hurt the imagination side of the equation in some people.
I prefer to give up DM control in a situation like this. Let them get away with blasting the door with fire or attacking it with weapons or whatever. It's clearly fun to use these elements in new ways, so encourage the fun. Just ramp up the difficulty of the next part, if you thought they got through it too easily. You're the DM, after all, nothing you haven't already said is set in stone.