Listened to a great interview with Parker Lewis (by Preston Pysh) talking about the Havening (on the "We Study Billionaires" podcast).
He made some really interesting points about why this creates such pricing pressure: much more than simply because supply of new Bitcoins are reduced by the 50% reduction in the block reward.
The other part of this is because the demand needs to get more supply from those already holding Bitcoin, and the only way to unlock more of this supply, is by paying more for it. Yet many Hodlers aren't looking to sell for any price (or at least not for many multiples beyond this price). So the bidding has to go higher and higher for more supply to meet even the exact same demand that exists prior to the Havening.
This is also why there is a lot of price volatility in Bitcoin, because it is TRUE price discovery. The existing financial system has a huge amount of opacity in it, with so many layers, and rent seekers involved, that there is simply no way to know the true market price of anything. Whereas with Bitcoin, its much cleaner, and direct, so what someone is willing to pay, and the price someone is wiling to sell for, is much more transparent.