How can we trust supply won't be increased by just a few lines of code?
The bitcoin network is composed of 'bitcoin full nodes', which are computers located all around the world, each one running independently to verify the state of the network.
Part of that verification includes making sure that the right number of coins are being created with each passing block, such that the total number of coins in existence is known, and predictable.
To change this 'coin issuance schedule', you would have to change the code running on all of those computers, so that they would all independently agree on some new issuance schedule, and could all continue to verify which blocks are valid (or not), in independent consensus. If you could only change the code on some of those computers, then those computers would start to follow blocks which the remaining bitcoin network nodes would consider invalid, effectively creating an altcoin-fork of the network (similar to what happened with 'bitcoin cash').
Anybody, at any point in time, could create some software that changes the issuance schedule. Thats easy. The hard part is convincing everyone that is running a bitcoin full node to switch to this new code, which creates more coins. Nobody has the authority to push such a change onto the network (top-down governance), rather it is the independent choices of all of the network's nodes (bottom-up governance) that defines the network.
So the answer is that you don't have to trust someone to not increase the supply. You just have to run some code that will verify that they haven't.
Well, the title is the only question, how can we trust supply wont be increased by just a few lines of code?
Just don't make any such changes to your code and you will never see an increased supply. You control the code running on your computer. If you never want to see an increased supply, never change your code in that way.
You can, of course, only interoperate with people who also don't want to see an increased supply. So the real issue has nothing to do with changes in code, it has to do with wanting a guarantee that there will still be people who don't want changes in the supply for you to interoperate with.
But you cannot ever force anyone to interoperate with you if they don't want to.
The bitcoin network is composed of 'bitcoin full nodes'... to change this 'coin issuance schedule', you would have to change the code running on all of those computers
Regardless of how many times this statement is repeated (and upvoted on SE!), it is obviously wrong to anyone willing to spend even a few minutes thinking about it.
Except for a few special ones (like ones that happened to be running at Coinbase and other influential places like that), full nodes have no influence on the block chain whatsoever. Nodes do not create blocks, miners do. It is the code that is running on the miners' machines that matters. And, at some point, incentives will align for the miners to do something to replace revenue from the waning block rewards, and the politics will incentivize the few influential nodes to follow this new chain since it will have the hashpower behind it (continuing to follow an underpowered chain could have disastrous results).
If you still believe that full nodes matter at all, consider this: there are generally 10's of thousands of full nodes on the network at any given moment. I could, sitting here at my desk, easily spin up 100,000 full nodes and get them integrated into the network within the next 24 hours without even maxing out my credit cards. I would then control the vast majority of full nodes. So why don't I do this? (Or more importantly, why doesn't anyone else with more resources than me do it?) Because there is no benefit to controlling any number of non-influential nodes. None. There are only a few dozen nodes on earth that matter, and they are the only ones that matter, and they are controlled by a small number of people who may someday have incentives to allow the increase the supply of bitcoins.
See longer answer here... https://bitcoin.stackexchange.com/a/108202/113175
Note that it is very likely that this answer will be heavily downvoted and will attract comments vehemently scolding me for being an idiot- while never offering any actual rebuttal to my argument. This too is a signal!