The popular intuition is that that greater supply = less demand. I've looked around and haven't found a counter-argument. Why is the BTC gaining value as its quantity increases?
The popular intuition is typically correct in well-saturated markets, but Bitcoin is not yet a well-saturated market. Though the supply of Bitcoin is currently increasing the demand is increasing dramatically faster. This is because we are during the initial adoption curve of a new technology and new demand is created as individuals discover the new tech.
In short, there is absolutely some downward pressure on Bitcoin's price exerted by the inflating supply, but it has been completely overwhelmed by upward pressure from new adoption.
The rate of bitcoin growth is regulated by virtue of how it was built such that each block should be found on average every 10 minutes, and the difficulty of mining is adjusted up or down to keep that rate more or less in line. Since the rate of production cannot be increased by brute force (by adding more computing power to the network) over the long run, there will no doubt be an increase in demand which is growing at a faster rate than the increase in supply. Of course the supply is fixed but the last bitcoin won't be mined for 100 years, so that shouldn't really play a factor today but that the rate of production will regulate.
If the ultimate amount were the regulating factor, then natural resources such as oil, rare earth metals or even gold should shoot to the moon because we know they will be exhausted in the next few centuries.
The supply of Bitcoin is increasing at a decreasing rate. If the supply curve just went to infinity, Bitcoin would be less attractive over time. But it doesn't: How many bitcoins will there eventually be?