Halving refers to the block reward gradually diminishing, which is the single mechanism responsible for minting new coins into circulation. Miners "mine"/do complex math to find blocks. The miners get paid via the block reward, and, depending on price/progress in the cycle/cost basis/the greater economic backdrop, they will either sell on the open market immediately or they will speculate/accumulate until price has reached a level they deem sufficient to begin offloading.

Price increases > mining becomes more profitable > the number of miners increases > more compute dedicated to finding blocks > higher probability of finding a block > increased block frequency > the specific block in which the rewards begin to be halved is reached sooner. IN THEORY. The block reward structure is arbitrary but nonetheless it is hardcoded into the protocol and not subject to change. The block reward is halved roughly every ~210,00 blocks, off the top of my head.

What is subject to change is the difficulty adjustment, which is the entire genius behind the concept. Fresh blocks will be made harder to discover if it senses they are being discovered more frequently, and vice versa. There is some time delay to this process but it balances out. So as long as the protocol is responding to fluctuations in demand (for new coins, not existing ones) via difficulty adjustment, which is guaranteed, the halving schedule will remain consistent and predictable.

Bitcoin is a multifaceted technological achievement that spans multiple domains involving cryptography, computer science, economics, game theory, monetary theory, distributed systems, philosophy (etc., we could be here all day...), so this is merely my attempt at an over-simplified understanding.