My answer as a DM would be simple.
'I do not believe off-hand you toss a spear two-handed, but if you can show me footage of, say a javelin thrower, or other spearman -realisticly- tossing such a weapon with two hands, then I'd certainly allow it! Anime doesn't count.'
If I was really generous, I'd substitute a live demonstration by the player in question.
You are correct, they typically thrown with one hand. With that in mind if you watch the Viking vs Samurai episode of Deadliest Warrior they do a demonstration of how the Vikings used to throw two spears at once.
Viking vs Samurai