I actually don't fully understand the reasons for why the pro-segwit side doesn't want to increase the block size (even beyond 2MB), except that it's a slippery slope: with Bitcoin, every time you change the block size it requires a hard fork.
Increasing the block size isn't a long-term solution, because there's always going to be some new ceiling. Eventually increasing the block size will become impractical.
As an aside, some coins have a variable block size to deal with this. AFAIK Monero is the only "major" coin which features variable blocks. It's also the only coin that's actually private.