I had a similar debate with a player once. Set the Wayback Machine 3 editions ago. I'd made a Gnome Fighter. As per the rules, a Gnome has to use a size Medium weapon in two hands. I chose the Bastard Sword, which has two stat lines in 2e. One-Handed and Two-Handed. Both are listed as size Medium. So I show up at the game with my bastard sword wielding Gnome with 18/31 Strength (another point of contention, but I pointed out Gnomes have no penalty to Strength in 2e, so there's no reason they can't have exceptional Strength).
When I started doing 2d4 damage for using the sword in two hands, the other player (not even the DM) flipped and tried to say that was the rules for a Medium sized character wielding the weapon in two hands. We went back and forth, but hey, if you insist...
I then revealed I'd taken the Two-Handed Weapon Fighting Style Specialization from the Complete Fighter's Handbook, to lower my speed factor by 3 when wielding a two handed weapon. "But if my wielding a bastard sword isn't considered to be the two handed version, then I get +1 damage for wielding a one handed weapon in both hands, so I'll go from 2d4 to 1d8+1".
The DM was happy to let me have my 2d4 damage, so Royle Gladdenstone eventually went down in history as "The World's Strongest Gnome".
Honestly, I didn't understand the fuss at the time, as Two Weapon Fighting was vastly superior in 2e. How times have changed, lol.