Increasing the blocksize to increase the transaction capacity of the network will also increase the storage and bandwidth requirements for running a "full node" of bitcoin.
Core believes that this would be bad for bitcoin because it would mean fewer people are "verifying" all the transactions, causing a bit more centralization in terms of trusting fewer miners and full nodes.
The big blockers believe that the network will survive and remain decentralized, and giving up a bit in terms of storage and bandwidth costs is worth it for faster/more transactions with lower fees.
The sneaky thing in this argument is that it is tacitly assumed that a full node has something to do with 'decentralization'. It hasn't. One should distinguish "decentralization" (which is a notion of *decision power*) and "distribution" (which has to do with spread-out architecture of a system). Facebook is entirely centralized (the power is with 1 entity, Mark Zuckerberg) but is very much distributed throughout the world.
To measure the power of "decentralization" of a full node, one has to ask oneself what *decision power* it has in bitcoin. What are the decisions in bitcoin ? They are the block chain.
All decisions in bitcoin are in the block chain: the block chain contains all the data on which bitcoin's existence is based. There's nothing in bitcoin of any significance that is not notified in the block chain.
So, how much can a full node take decisions ?
The block chain of bitcoin is supposed to be built according to a certain set of rules: the protocol. Full node software checks the entire block chain to see whether this protocol has been followed or not. The protocol rules are built into the software of the full node. So at first sight, it could seem that
full nodes can signal that the block chain one is giving to them, is not built according to the protocol. That's true: it can SIGNAL it, to its owner.
Essentially, we can assume that a certain part of the block chain, since its beginning, is built according to the protocol in the software of the full node. And at a certain point, say, block 515000, the block in the block chain is NOT according to the rules. What does the full node do ?
It refuses that block 515000, and it waits until it finds a "correct" successor to block 514 999, the last "good" block.
Now, who is MAKING the block chain ?
The only entities MAKING the block chain are the miners. In order to make a block chain, one needs to prove HUGE amounts of work, so only miners can possibly propose blocks which contain this huge amount of work. Nobody else can. Miners validate previous blocks, by building their blocks on top of the block they validate.
That is the core of the consensus decision mechanism in bitcoin: a block is validated by other miners, because they build their blocks on top of it.Given that only miners can validate blocks, and that, if they do, they build blocks on top of the valid blocks, it means that as long as they have consensus amongst them, there is only one block chain out there, and nobody can make another one.
So if your "validating node" somehow doesn't like block 515 000, the only unique block 515 000 out there on which miners built 515 001 and 515 002 etc..., then your validating node stops forever at 514 999, and that's it. Now you know. And you knowing is the only thing that happens. Your node stopping at 514 999, or you switching off the computer on which it runs, has, from the outside, exactly the same effect.
You have no decision power that goes beyond "switching off your computer".This is why full nodes have no decision power on the decisions in bitcoin, that is to say, on the construction of the block chain ; and nodes that have no decision power do not contribute to decentralization.Bitcoin was made that way: the decision power is the consensus decision, which is made with proof of work (miners), not with nodes (because nodes can be Sybil attacked). The decision is made by building on top of a block which the provider of proof of work deems valid ; to be, himself, validated by the next block built on top of him etc....
Full nodes can essentially do two things:
1) copy the unique block chain that is out there and serve as a proxy server for it
2) disagree and stop, waiting forever for something that will not come
This is why, even in 2010, Satoshi already said that "the only people needing to run full nodes are those wanting to make new coins" (mining). The decentralization of bitcoin resides in those that make the block chain. There are about 20 of them. That's the real "decentralization" of bitcoin, not whether some guy in central Africa has a full node running in his basement.