Why would people invest loads of money in BTC after the halving and not before?
People choose to invest in the BTC market post-halving due to a reduction in its supply, which will increase demand, and you know that when supply becomes low and people demand anything high, it increases price pressure.
...when halving is happening Bitcoin supply is cut into half, meaning that the scarcity will make price to increase.
Those are repeating a very common misconception.
First, the supply is not reduced by the halving. Instead, the
increase in supply is reduced. The supply increases with every block until it reaches 21 million.
Second, reducing the supply does not increase the demand. In general, supply and demand are independent functions.
You're right. The halving is not about the Bitcoin supply being cut in half, etc. However, to avoid further misconception it's better to explain this way.
The halving is an act of creating or maintaining BTC scarcity and it's technically an act of splitting in half the miner's reward.
It's a policy created by Satoshi to counteract inflation in the market to increase demand.