Since 1.6.1 (13w25b), swords can no longer be used to break blocks in creative mode. This is (presumably) so the player doesn't accidentally break blocks while attacking with a sword. Since 1.9, axes double as weapons, however they can still be used to break blocks, leading to the same problem that the 1.6.1 change was intended to solve.
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It's still in 1.14.2 release, but iirc, it should be only swords that can't break (most) blocks in creative when you hold them, I just can't find the source (Twitter? Snapshot post?) where it possibly was mentioned. I know one can't take the MC Gamepedia as reliable source, there has been wrong or insufficient information on that inofficial MC-Wiki in the past, but anyway, on there it's only the sword mentioned to have that kind of security measure for Creative: https://minecraft.gamepedia.com/Sword#Safety_around_constructions, so axes breaking blocks in Creative should be very likely WaI?
Thinking about it, I suppose this could be working as intended. It would be confusing for a player trying breaking wooden blocks with an axe. But at the same time, it is annoying to accidentally break blocks when misclicking while fighting a mob with an axe.