Understanding a UASF requires understanding where hashrate comes from. Bitcoin is very clever in that hashrate costs money, and not just a little money, it costs a lot of money.
Which chain has more work is approximately saying 'which chain destroyed the most value in electricity'. The proof of work powering bitcoin costs hundreds of millions of dollars per year.
Nobody burns hundreds of millions per year for free. They do it because you receive Bitcoins as payment, and then you can go sell those Bitcoins to pay your electricity and hardware bills.
That means you have to be able to find someone willing to buy them. A UASF is a bunch of users saying 'we'll never buy your coins unless you follow our fork'. If only a few users say this, it's no big deal, and the miners can decide to listen to them, or they can decide not to bother.
But if 2/3rds of the userbase all agree to enforce the UASF, the miners suddenly are going to have a lot of trouble selling their non-UASF coins. Enough trouble that they probably can't pay their electricity bills. Even worse for the miners, the UASF chain has a high block reward, so they know that if they do mine the UASF chain, they actually will be able to pay their bills. And if a competing miner does it, that competing miner will have much higher margins, higher profits, and will be able to out-invest you when it comes to buying more hashrate.
Scariest of all, if the UASF chain ends up with more work than the non-UASF chain, the non-UASF chain gets completely obliterated, and its full transaction history is reversed, and all the blocks you mined as a miner are destroyed. So even if the UASF doesn't seem to have majority support, it's really bad for you as a miner and as a user if it ever eventually does gain majority support. So when the UASF has a lot of traction, really the safest move is to join the UASF, because at least then your coins aren't at risk of being eliminated entirely.