Wjy does Robin use a hammer to fight?

I'm not sure when and how he is supposed to have had training in mounted combat anyway - knights spent years perfecting their skills. As a longbowman he'd be more adept at infantry combat, using a falchion or similar short sword for a backup close quarters weapon.

That was generally the hand weapon of an archer. It would actually be illegal for him to use a sword, as swords are heraldic arms. it would also be pointless, as swords require a lot of training. A longbowman would definitely use a maul.

For the reason that commoners tended to fight with whatever they could get. He would not necessarily have been trained with a sword, and sword play is more difficult to manage properly than swinging a hammer, if that is what he has done all of his life.

Also, his father was a stone mason, with some interesting pre-Masonic philosophical conceits. The hammer has ever been a symbol in masonry - and a longbow, when drawn, makes the same shape as a compass...

cur. adv. vult

It's actually historically accurate. https://en.wikipedia.org/wiki/War_hammer

The reason to use it is that it was very hard to injure someone decked out in chainmail and armor, only a direct thrust of a sword could really do the job. For close hand to hand combat you needed something that could injure your opponent when struck against his protection.

Sorry you don't like the movie, I think it's great!

While technically the hammer he uses is a few centuries too modern, blunt force weapons were far more common than you usually see in films.
In all likelihood the majority of commoner footmen and archers (who doubled as footmen when needed) would've used mainly spears for the dedicated infantry and then axes, falchions, maces, polearms,...
Swords were the sidearm of the wealthy, and iirc even in this period many nobles would've begun replacing them with other weapons more suited to an anti-armour role.